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"What’s In A Name?\n“No race in the world prizes lineage so highly as the Arabs and none has kept its blood so pure.”\nWilfred Thesiger, Arabian Sands, 1959\nOne of the first challenges in arriving in the Middle East is trying to decode and pronounce the long names. It seems rude and lazy to mumble them or to avoid saying them altogether, and worse yet to call people by the wrong names. When I first started teaching, I was so daunted by the fifteen seemingly identical men in white gowns (thobes) and headscarves in my class with their complicated names, that I wrote notes to myself about their appearance and my own version of a pronunciation system, so I could sort them out. Saleh: “SAY-luh, with the sharp wit and expressive face”. Jalal: “Juh-LAL- easy-going manner and smiling eyes”. Ahmad: “AH (with a little coughing sound)-med, who asks many questions”. Fortunately, one only needs to call them by their first names!\nI soon learned that there is indeed a pattern to Arabic names. For men, “bin” ( or “ibn”) following the first name means “son of” and is followed by the father’s first name, which is then followed by “al” which means “from the family of.” For example, the sheikh of Dubai is Mohammed bin Rashid al Maktoum. His father was Rashid bin Saeed al Maktoum. One of Sheikh Mohammed’s sons is Hamad bin Mohammed al Maktoum. The Qatar “emir,” another term for sheikh used more frequently among Qataris, is Hamad bin Khalifa al Thani. His father was Kahlaifa bin Hamad al Thani. One son of the Emir is Tamin bin Hamad al Thani. There are only a few Arab names. Mohammeds, Khalifas, Thanis, Hamads, Abdullahs, and Hassams abound. Therefore, this naming system allows one to unravel the puzzle of a person’s lineage. And family is absolutely central in the Arab culture, the key to a person’s identity, the most important of all qualifiers.\nIt is interesting to note that women keep their father’s family names when they marry. After a woman’s first name is “bint” followed by her father’s first name, then “al” referring to the father’s family name. For example, the third wife of Sheikh Mohammed is Haya bint Hussein. (She is the daughter of the late King Hussein of Jordan.) The second wife of the Emir of Qatar is Mozah bint Nasser al Missned. This custom means that a couple never has the same family/last name, unless they are cousins, a common arrangement in royal families, which makes things even more confusing! A child never takes on his mother’s family name. In fact, it is impossible to determine who the mother of any individual is in the Arab world unless you are a personal acquaintance or it is a famous, usually royal, family who has made its records public, which is rare. Thus, you will not be able to identify the mother of any individual.\nAt first, I found this strange, but I quickly realized I was over-simplifying, tangled up in cultural nuances and assumption. Many women in the United States keep their so-called maiden names and give their children either hyphenated last names or only their husbands’ names. In other words, they are joining what is called the patrilineal genealogical structure of Asia and the Middle East, where there are no recorded birth lines to the mother’s family. It is easy to get trapped into dualistic thinking. “They do it that way in the East. We do it this way in the West.” The lines are blurred. And there is no one right way.\nNext post: Construction in a Caravan Culture"

"From Dr. Wayne Baker: Please welcome Joe Grimm, a journalism professor at Michigan State University and editor of a new series of guides to cultural competence. Here’s the first book in the MSU series.\nAnd—here’s Joe Grimm …\nNames can be barriers.\nUntil you know a person’s name and how to say it, you might hold them at the verbal equivalent of arm’s length.\nIt happens with people whose name you can’t remember. It happens if the name is unfamiliar. The barrier can be rooted in culture, language or religion.\nWhen Living Textbook partner Emilia Askari and I began working with middle-school journalism students in Unis Middle School in Dearborn, Mich., we met a room full of people with names with which I had little familiarity. Most of the students there are Arab-American Muslims.\nIn my family, most people are named after relatives, saints or for qualities expressed in the names. Instead of Steven and Terry and Kyle, this class had Ali, Fatima and Khalil.\nAs an ice-breaker, I told the students my name and how I got it. I asked to hear the story of their names.\n“My name is Khalil, and there are multiple reasons on why I have my name. First, my name means friend of God. Second, my uncle’s name is Khalil.”\n“My name is Fatima. I was named that because it is the name of the prophet’s daughter. My name means the one kept away from evil and bad character.”\n“My name is Ahmad. That name means praiseworthy. My dad named me that because his brother that died was named Ahmad, too. My name is also one of the many names of the prophet Mohammed.”\nOne student, named Mohammed, said that there are so many boys at that school with his name that when someone calls it, “half the school turns around.” Having grown up with a lot of people named after Saint Joseph, I understood immediately.\nNames can be barriers, but they should be bridges.\nCare to learn more about this? In “100 Questions About Indian Americans,” first in a series of guides by Read The Spirit and the Michigan State University School of Journalism, one of the issues that comes up is names.\nWhose name presents a barrier to you?\nCan you get closer to them by learning its story or pronunciation?\nWhat names seem funny or odd to you? Do you know where they come from?\nPLEASE LEAVE A COMMENT BELOW:\n- Cultural Competence: Which generation has no majority race?\n- Cultural Competence: Is your name a barrier … or a bridge?\n- Cultural Competence: Is Johnny Depp’s portrayal of Tonto offensive?\n- Cultural Competence: Do you see yourself in biracial Cheerios family?\n- Cultural Competence: Can a Buddhist monk be an anti-Muslim Bin Laden?"

"There is a plethora of names for parents to choose from when considering what to call a child. Many parents assign traditionally masculine or feminine names to their children depending on their gender.\nHowever, others opt for names that can be attributed to either male or female children. These types of names are considered gender-neutral or androgynous. They can be used for either boys or girls and do not easily determine the gender of a child when looking at the name itself.\nAndrogynous names have different origin stories. Some were originally used as a boys or girls names but have lost their gender-specific identity over time while others have gained popularity in use for both boys and girls.\nAlternatively, some names were inspired by cities, nature or ideas and are not associated with gender at all. Continue reading below to learn more about the gender-neutral names, how they originated and what the most popular current androgynous names are.\nWhat Makes a Name Androgynous\nNot everyone unanimously agrees that certain names are gender-neutral. This can be due to the associations that people have with certain names. However, androgynous names are generally those that have been used as both girls’ and boys’ names and thus, are no longer associated with a specific gender.\nIn the English language, feminine and masculine names are typically differentiated by their endings. Names that are have been traditionally used for girls tend to end in “a”, “ey”, “ie”, “ee” and “ine.” For example, Christine is a name typically used for girls while Christopher is the male version typically used for boys. In addition, names related to flowers or plants such as Ivy, Holly and Daisy are also considered feminine.\nOn the other hand, names that do not carry any gender connotations are also considered androgynous. This is where parents can be more creative in their name choices and draw inspiration from a number of sources.\nFor instance, cities typically are not associated with gender. Thus, both boys and girls can be named Dallas, London, Phoenix or Hudson. Additionally, some parents find inspiration in nature and name their children things like Clover, Moon, Sage or Rain.\nOrigins of Unisex Names\nDifferent androgynous names have different origins. Many names, such as Addison and Billie, were once used predominantly for boys. Overtime, families began using them for daughters for various reasons.\nFurthermore, the same name can be used for different genders in different cultures and the blending of those cultures changed the connotations of those names. For instance, the name Ariel, which means “lion of God”, is a Hebrew name that is primarily assigned to boys. However, in the movie “The Little Mermaid,” Ariel was used as a girl’s name.\nWhile many other countries do not practice or permit families giving children unisex names, certain countries do name children without considering gender.\nFor instance, many African cultures involve naming children after events or circumstances in the family’s home. For Ayodele is a gender-neutral name that means “joy has come home.” Additionally, children names reflect moods or feelings. For instance, a child born during a happy time can be named Akatendeka which means faithful.\nHowever, in other countries like Iceland and Denmark, it is unlawful to give children gender-neutral names. Furthermore, there is a registrar of appropriate names in Germany.\nWhile many names evolved over time to be suited to both boys and girls, nowadays parents simply create name or pick words that make gender categorizing difficult. Some families select neutral names like Apple, Reign or Justice while others go against the grain and give their child a name that is traditionally considered opposite of their gender.\nTop 30 Gender Neutral Names"

"A unisex name (also known as an epicene name, a gender-neutral name or an androgynous name) is a given name that can be used by a person regardless of the person's sex. Some countries have laws preventing unisex names, requiring parents to give their children sex-specific names. In other countries unisex names are sometimes avoided for social reasons.\nNames may have different gender connotations from country to country or language to language. For example, the Italian male name Andrea (derived from Greek Andreas) is understood as a female name in many languages, such as German, Hungarian, Czech, and Spanish. Sometimes parents may choose to name their child in honor of a person of another sex, which – if done widely – can result in the name becoming unisex. For example, Christians, particularly Catholics, may name their sons Marie or Maria in honor of the Virgin Mary or their daughter José in honor of Saint Joseph or Jean in honor of John the Baptist. This religious tradition is more commonly seen in Latin America and Europe than in North America.\nSome masculine and feminine names are homophones, pronounced the same for both sexes but spelled differently. For example, Yves and Eve and (for some speakers) Artemus and Artemis. These names are not strictly unisex names.\nIn popular culture\nUnisex names can be used as a source of humor, such as Julia Sweeney's sexually ambiguous character \"Pat\" on Saturday Night Live. A running joke on the TV show Scrubs is that almost every woman J.D. sleeps with has a unisex name: Jordan, Alex, Danni, Elliot, Jamie, Kim, etc. Similarly, the sex of the baby Jamie in Malcolm in the Middle was purposely kept ambiguous when first introduced at the end of the show's fourth season leading to speculation that it would remain unknown. However, the character's sex was revealed at the end of the first episode of season five. In Gilmore Girls, Rory is bothered by the discovery that her boyfriend Logan's workmate Bobby, is female. Rory had assumed Bobby was male and it is only upon their first meeting that Rory discovers Bobby is female.\nIn Japanese dramas and manga, a unisex name may be given to an androgynous or gender-bending character as part of a plot twist to aid in presenting the character as one sex when they are actually another.\nIn mystery fiction, unisex names have been used to tease readers into trying to solve the mystery of a character's sex. The novels of Sarah Caudwell feature a narrator named Hilary Tamar, a law professor who is never identified as either male or female.\nUnisex names have been enjoying a decent amount of popularity in English speaking countries in the past several decades. Masculine names have become increasingly popular among females in the past century but feminine names remain extremely rare among males. An example of a feminine name which have been given to males is Carol. Examples of masculine names which have been widely given to females and thus have become unisex include Ashley, Beverly, Evelyn, Hilary, Jocelyn, Joyce, Kelly, Lynn, Meredith, Shannon, Shirley, Sidney, Vivian, and Whitney. Modern unisex names may derive from nature (Lake, Rain, Willow), colors (Blue, Grey, Indigo), countries or states (Dakota, India, Montana), surnames (Jackson, Mackenzie, Madison, Murphy), and politicians (Kennedy, Reagan). Examples of unisex names among celebrities include Jamie (Jamie Bell and Jamie Lee Curtis), Morgan (Morgan Freeman and Morgan Fairchild), Shannon (Shannon Leto and Shannon Elizabeth), Taylor (Taylor Lautner and Taylor Swift), Tracy (Tracy Morgan and Tracy Chapman), Jordan (Jordan Knight and Jordan Pruitt), and Hayden (Hayden Christensen and Hayden Panettiere). According to the Social Security Administration, Jayden has been the most popular unisex name for boys since 2008 and Madison has been the most popular unisex name for girls since 2000 in the United States. Prior to Jayden, Logan was the most popular unisex name for boys and prior to Madison, Alexis was the most popular unisex name for girls.\nMany popular nicknames are unisex. Some nicknames, such as Alex and Pat, have become popular as given names in their own right. The following list of unisex nicknames are most commonly seen in English-speaking countries such as Canada, the United States, Australia, South Africa, and the United Kingdom.\n- Alex - Alexander, Alexandra, Alexis, Alexandria, Alexa\n- Andi, Andie, Andy - Andrea, Andre, Andrew\n- Ash - Asher, Ashley, Ashlyn, Ashton\n- Berni, Bernie, Berny - Berenice, Bernard, Bernadette\n- Berti, Bertie, Berty - Albert, Alberta, Alberto, Robert, Roberta, Roberto\n- Bobbi, Bobbie, Bobby - Robert, Roberta, Roberto\n- Cas - Casper, Cassandra, Cassian, Cassidy, Castiel\n- Cassi, Cassie, Cassy - Casper, Cassandra, Cassian, Cassidy\n- Charli, Charlie, Charly - Charlene, Charles, Charlotte\n- Chris - Christian, Christine, Christina, Christoph, Christopher\n- Christi, Christie, Christy - Christine, Christina, Christopher\n- Danni, Dannie, Danny - Daniel, Danielle\n- Ed, Eddi, Eddie, Eddy - Edith, Edmund, Edward, Edwin, Edwina\n- Fran - Frances, Francis, Francesca, Francesco, Francine\n- Franki, Frankie, Franky - Frances, Francis, Francesca, Francesco, Francine, Frank, Franklin\n- Franni, Frannie, Franny - Frances, Francis, Francesca, Francesco, Francine\n- Freddi, Freddie, Freddy - Fred, Frederick, Frederica\n- Gabbi, Gabbie, Gabby - Gabriel, Gabriella, Gabrielle\n- Georgie - George, Georgeanna, Georgette, Georgia, Georgina\n- Izzi, Izzie, Izzy - Isaac, Isabel, Isabella, Isabelle, Isidore, Isolde, Elizabeth\n- Jacki, Jackie, Jacky - Jack, Jackson, Jacqueline, John\n- Jay - Jacob, James, Jamie, Jane, Jayden, Jaeden\n- Jess - Jesse, Jessica\n- Jerri, Jerrie, Jerry - Gerald, Geraldine, Gerard, Jeremiah, Jeremy, Jerome\n- Joey - Joanna, Joanne, Joseph, Josephine\n- Joss - Jocelyn, Joseph, Josiah\n- Kel - Kelly, Kelsey\n- Kris - Kristin, Kristina, Kristine, Kristopher\n- Les - Leslie, Lester\n- Liv - Olive, Oliver, Olivia\n- Lou - Lewis, Louis, Louise, Lucas\n- Louie - Louis, Louise\n- Maddi, Maddie, Maddy - Madeline, Madison\n- Mandi, Mandie, Mandy - Amanda, Amandus, Mandel\n- Manni, Mannie, Manny - Emanuel, Emmanuel, Emmanuelle, Manfred\n- Matti, Mattie, Matty - Mathilda, Matilda, Matthew\n- Max - Maximilian, Maximus, Maxine, Maxwell\n- Mel - Melanie, Melinda, Melissa, Melody, Melvin, Melina\n- Micki, Mickie, Mickey, Micky- Michael, Michaela, Michelle, Mikayla\n- Nat - Nathanael, Natalia, Nathalie, Natasha, Nathan, Nathaniel, Natalie\n- Nicki, Nickie, Nicky - Nicholas, Nicola, Nicole, Nicolette, Nikita\n- Oli, Olli, Ollie, Olly - Olive, Oliver, Olivia\n- Pat - Patricia, Patrick\n- Patti, Pattie, Patty - Patricia, Patrick\n- Robbi, Robbie, Robby - Robert, Roberta, Roberto, Robin\n- Ronni, Ronnie, Ronny - Ronald, Veronica\n- Sacha, Sascha, Sasha - Alexander, Alexandra\n- Sal - Sally, Salvador\n- Sam - Samson, Samuel, Samantha\n- Sammi, Sammie, Sammy - Samson, Samuel, Samantha\n- Sandi, Sandie, Sandy - Alexander, Alexandra\n- Shelli, Shellie, Shelly - Michelle, Sheldon, Shelton\n- Stevie - Stephanie, Stephen, Steven\n- Terri, Terrie, Terry - Terence, Teresa, Theresa\n- Theo - Theobald, Theodora, Theodore, Theodoros\n- Toni, Tonie, Tony - Anthony, Antonio, Antonia\n- Val - Valentina, Valentine, Valentino, Valerie\n- Vic - Vicky, Victor, Victoria\n- Viv - Vivian, Viviana, Vivien, Vivienne\nFinnish law bans giving \"female child a male name and male child a female name\" among other restrictions. Some ambiguous names do exist, which have been given to children of both sexes. A partial list includes: Aala, Aale, Aali, Aalo, Airut, Aleksa, Alvi, Ami, Ara, Ariel, Asla, Dana, Dara, Eedi, Eelia, Eeri, Eeti, Eka, Ellis, Emili, Ensi, Ervi, Essa, Hami, Hani, Heile, Heine, Helgi, Helle, Hille, Ila, Ille, Ilo, Jessi, Jo, Juno, Kaari, Kaiho, Kara, Karli, Karo, Kullero, Lahja, Lei, Lemmi, Lumo, Mara, Margo, Marin, Marjus, Mietti, Mille, Miska, Mitja, Muisto, Nevin, Niika, Niki, Nikita, Nikola, Nilla, Noa, Noe, Noel, Oma, Orla, Peeta, Rani, Reine, Reita, Rene, Sana, Sani, Sasa, Sasha, Sassa, Seri, Sire, Sirius, Soini, Soma, Sävel, Tiera, Toive, Vanja, Varma, Veini, Vendi, Venni and Vilka. Many of these names are rare, foreign or neologism, established names tend to be strongly sex-specific. Notably, a class of names that are derived from nature can be often used for either sex, for example: Aalto (wave), Halla (frost), Lumi (snow), Paju (willow), Ruska (fall colors), and Valo (light). Similarly, there are some (sometimes archaic) adjectives which carry no strong gender connotations, like Kaino (timid), Vieno (calm) or Lahja (a gift).\nPopular unisex names of French origin include Camille, Claude, and Dominique. There are also pairs of masculine and feminine names that have slightly different spelling but identical pronunciation, such as André / Andrée, Frédéric / Frédérique or Gabriel / Gabrielle. In France and French-speaking countries, it can happen for people to have a combination of both masculine and feminine given names, but most of these include \"Marie\", such as Jean-Marie, Marie-Jean, Marie-Pierre. Marie was a unisex name in medieval times; it is nowadays only female except for its presence in compound names. Notable examples of people with a combination of masculine and feminine given names are Jean-Marie Le Pen (male), Marie-Jean Hérault de Séchelles (male), Marie-Pierre Kœnig (male), and Marie-Pierre Leray (female).\nEuropean royals often bear the name Marie, the French form of Maria, in their names. Prince Amedeo of Belgium, Archduke of Austria-Este (Amedeo Marie Joseph Carl Pierre Philippe Paola Marcus), Prince Jean of Luxembourg (Jean Félix Marie Guillaume), and Jean, Grand Duke of Luxembourg (Jean Benoît Guillaume Robert Antoine Louis Marie Adolphe Marc) are examples of male royals who bear Marie in their names.\nIn the past, German law required parents to give their child a sex-specific name. This is no longer true, since the Federal Constitutional Court of Germany held in 2008 that there is no obligation that a name has to be sex-specific, even if it is the only one. The custom to add a second name which matches the child's legal sex is no longer required. Still unisex names of German origin are rare, most of them being nicknames rather than formal names. Examples for unisex names: Eike, Gustl (the male variant is a shortening of August or Gustav, the female for Augusta), Toni, Kai.\nMany of the modern Hebrew names are unisex. A few popular examples are Gal, Tal, Noam and Daniel (which is unisex only as a modern name).\nUnisex names are illegal in Iceland (the given name Blær the only known legal exception). The Icelandic Naming Committee (ice. Mannanafnanefnd) has preapproved male and female lists.\nAdditionally traditional patronymic (or rarely matronymic or both) Icelandic last names (by law) can't be unisex. The suffix of the last name -dóttir (e. daughter) gives away the female sex. Males use the suffix -son (rare exceptions for foreign females; when using husbands last name as a family name; family names are in general illegal with few exceptions). Given names are also clearly masculine or feminine (to Icelanders) and linguistic gender has to match the gender identity of the person.\nAs of 2012[update], the law has been successfully challenged once, for the given male name Blær (transliterated Blaer) allowing for that one exceptionally used for females. The Icelandic Naming Committee had for 14 years rejected a girl to have her registered as Blaer in the national census, keeping her registered with the default given name stelpa (e. girl) - the name was not on the list of about 1,853 approved female names. A lower court deemed the name additionally legal for females and the state decided not to use its right to appeal.\nFew exceptions apply for linguistic gender such as the traditional name Sturla, linguistically feminine, from medieval history always applies to males and Ilmur (e. fragrance or odour), linguistically masculine, must apply to females.\nMany Indian names become unisex when written with Latin characters because of the limitations of transliteration. The spellings Chandra and Krishna, for example, are transliterations of both the masculine and feminine versions of those names. In Indian languages, the final a's of these names are different letters with different pronunciations, so there is no ambiguity. However, when they are seen (and usually, spoken) by someone unfamiliar with Indian languages, they become sexually ambiguous. Other Indian names, such as Ananda, are exclusively or nearly exclusively masculine in India, but because of their a ending, are assumed to be feminine in Anglophone societies. Many unisex names in India are obvious and are never ridiculed. For instance Nehal, Sonal, Snehal, Niral, Pranjal and Anmol are used commonly to name baby boys or girls in western states of India such as Gujarat. Similarly, names like Kajal,Sujal, Viral, Harshal, Deepal, Bobby, Mrinal, Jyoti, Shakti, Kiran, Lucky, Ashwini, Shashi, Malhar, Umang, Shubham and Anupam are also very common sex-neutral names or unisex names in India. Most Punjabi Sikh first names such as \"Sandeep, Gurdeep, Kuldeep ,Mandeep\", \"Surjeet, Gurjeet, Kuljeet, Harjeet, Manjeet\", \"Harpreet, Gurpreet, Jaspreet, Kulpreet, Manpreet\", \"Prabhjot, Harjot, Gurjot, Jasjot\" and \"Sukhjinder, Bhupinder, Jasbinder, Parminder, Kulvinder, Harjinder, Ranjodh, Sheeraz, Hardeep, Kirendeep, Sukhdeep, Govindpal, Encarl, Rajan\" are unisex names and equally commonly given to either sex. Also, names derived from Dari Persian and Arabic, but not used among native speakers of those languages, are common among South Asian Muslims. Since Persian doesn't assign genders to inanimate nouns, some of these names are gender-neutral, for example: Roshan, Parveen, and Insaaf.\nUntil 2012 it was illegal to give unisex names to children.\nCommon Italian boys' names, such as Nicola or Luca, are assumed to be feminine in English, due to the 'a' termination. This also happens to several masculine names ending with 'e', like Simone, Gabriele, Michele, Davide or Daniele.\nThe name \"Andrea\" in Italy is a male name but it may be used, even if it rarely happens.[clarification needed]\nDespite there being only a small number of Japanese unisex names in use, unisex names are widely popular. Many high-profile Japanese celebrities such as Hikaru Utada, Jun Matsumoto, Ryo Nishikido, Tomomi Kahala, Harumi Nemoto, Izumi Sakai, and Shizuka Arakawa have unisex names.\n- Ryou (Ryoo, Ryō, Ryota)\n- Shou (Shoo, Shō)\n- Yuu (Yu, Yū, Yuuya, Yuna)\n- Yuuki (Yuki, Yūki)\n- Yoshi (Yoshie, Yoshio)\nUnisex names may also be used as nicknames. For example, a man named Ryounosuke and a woman named Ryouko may both use the unisex name Ryou as a nickname.\nNames that end with an i are considered unisex in Brazil. They tend to be Native Brazilian Indian names in origin, such as Araci, Jaci, Darci, Ubirani, but names from other cultures are now being absorbed, such as Remy, Wendy, and Eddy. Names that end with ir and mar tend to be unisex also, such as Nadir, Aldenir, Dagmar and Niomar - though in these cases there are some exceptions.\nCommon Russian boys' names, such as Nikita and Misha (short for Mikhail), are assumed to be feminine in English, due to the 'a' termination, which is actually common in diminutive masculine forms. However, the 'a' termination does hold true for other Russian contexts, as the letter 'a' is appended to all Russian female last names (Ivanov's mother, wife, and daughter all have last name Ivanova; yet any son born out of wedlock to an Ivanova defaults back to last name Ivanov), and nearly all Russian feminine first names end in 'a' (or 'ya', a distinct letter in the Cyrillic alphabet). Also, nicknames (shortened versions of names) can be sex-ambiguous: Sasha/Shura (Alexandr or Alexandra), Zhenya (Yevgeniy or Yevgeniya), Valya (Valentin or Valentina). In all cases a noun ending in -a or -ya is declined as if it were feminine no matter the actual gender.\nIn Spain unisex names are extremely rare. In Valencia and Catalonia though, the name Pau was used both for boys and girls from the mid-70s. María, an originally feminine name is used for males as middle name, very commonly after José (e.g., José María). José is used for females preceded by María (María José).\nThere are many Turkish names which are unisex. These names are almost always pure Turkish names (i.e. not Turkified Arabic names that have an Islamic connotation) that derive from Turkish words. These names may either be modern names or be derived from Turkic mythology. Among the common examples of the many unisex names in Turkey include, Aytaç, Ayhan, Bilge, Cemre, Derya, Deniz, Evren, Evrim, Göksel, Gökçe, Özgür, Turhan, Toprak, Yüksel or Yücel. Some Persian-derived Turkish names, like Can and Cihan, are also unisex, as are even a few Arabic-derived names, like İhsan and Nur.\nAmong modern Vietnamese names, unisex names are very popular. Vietnamese tend to distinguish unisex names by middle names (for example Quốc Khánh is a male name and Ngân Khánh is a female name). In many cases, a male could have a female name and vice versa. Popular examples of unisex names in Vietnam are: Anh (beautiful or outstanding), An (safe and sound), Hà (river), Khánh (joy or virtue), Linh (divinity, essence, or spirit), or Tú (star), etc.\n- \"Rory and Logan: Getting Serious\". Crushable. Retrieved 23 June 2012.\n- Jayden at BehindtheName.com\n- Madison at BehindtheName.com\n- Logan at BehindtheName.com\n- Alexis at BehindtheName.com\n- \"FINLEX ® - Ajantasainen lainsäädäntö: 9.8.1985/694\" (in Finnish). Finlex.fi. Retrieved 2013-09-29.\n- \"Lapsesta Ruu tai Sirius? Sukupuolineutraaleista nimistä tuli buumi | Helsingin Uutiset\" (in Finnish). Helsinginuutiset.fi. Retrieved 2013-09-29.\n- French Unisex Names at About.com\n- French First Names at About.com\n- \"Oh no, you can't name your baby THAT!\" CNN.com\n- Flippo, Hyde \"The Germany Way\" Published by McGraw-Hill (1996), Pages 96-97\n- BVerfG, 1 BvR 576/07 vom 5.12.2008, paragraph 16\n- \"Name Law and Gender in Iceland\" (PDF). UCLA Center for the Study of Women. 9 June 2009. Retrieved September 7, 2014.\n- \"Icelandic girl Blaer wins right to use given name\". BBC. 31 January 2013. Retrieved 7 September 2014.\n- Sikh Names (SikhNames.com) Sikh Names, Meanings & Pronunciation"

"A unisex name (also known as an epicene name, a gender-neutral name or an androgynous name) is a given name that can be used by a person regardless of the person's sex. Some countries have laws preventing unisex names, requiring parents to give their children sex-specific names. In other countries unisex names are sometimes avoided for social reasons.\nNames may have different gender connotations from country to country or language to language. For example, the Italian male name Andrea (derived from Greek Andreas) is understood as a female name in many languages, such as German, Hungarian, Czech, and Spanish. Sometimes parents may choose to name their child in honor of a person of another sex, which – if done widely – can result in the name becoming unisex. For example, Christians, particularly Catholics, may name their sons Marie or Maria in honor of the Virgin Mary or their daughter José in honor of Saint Joseph or Jean in honor of John the Baptist. This religious tradition is more commonly seen in Latin America and Europe than in North America.\nSome masculine and feminine names are homophones, pronounced the same for both sexes but spelled differently. For example, Yves and Eve and (for some speakers) Artemus and Artemis. These names are not strictly unisex names.\nIn popular culture\nUnisex names can be used as a source of humor, such as Julia Sweeney's sexually ambiguous character \"Pat\" on Saturday Night Live. A running joke on the TV show Scrubs is that almost every woman J.D. sleeps with has a unisex name: Jordan, Alex, Danni, Elliot, Jamie, Kim, etc. Similarly, the sex of the baby Jamie in Malcolm in the Middle was purposely kept ambiguous when first introduced at the end of the show's fourth season leading to speculation that it would remain unknown. However, the character's sex was revealed at the end of the first episode of season five. In Gilmore Girls, Rory is bothered by the discovery that her boyfriend Logan's workmate Bobby, is female. Rory had assumed Bobby was male and it is only upon their first meeting that Rory discovers Bobby is female.\nIn Japanese dramas and manga, a unisex name may be given to an androgynous or gender-bending character as part of a plot twist to aid in presenting the character as one sex when they are actually another.\nIn mystery fiction, unisex names have been used to tease readers into trying to solve the mystery of a character's sex. The novels of Sarah Caudwell feature a narrator named Hilary Tamar, a law professor who is never identified as either male or female.\nUnisex names have been enjoying a decent amount of popularity in English speaking countries in the past several decades. Masculine names have become increasingly popular among females in the past century but feminine names remain extremely rare among males. Examples of masculine names which have been widely given to females and thus have become unisex include Ashley, Beverly, Evelyn, Hilary, Jocelyn, Joyce, Kelly, Lynn, Meredith, Shannon, Shirley, Sidney, Vivian, and Whitney. Modern unisex names may derive from nature (Lake, Rain, Willow), colors (Blue, Grey, Indigo), countries or states (Dakota, India, Montana), surnames (Jackson, Mackenzie, Murphy), and politicians (Kennedy, Madison, Reagan). Examples of unisex names among celebrities include Jamie (Jamie Bell and Jamie Lee Curtis), Morgan (Morgan Freeman and Morgan Fairchild), Shannon (Shannon Leto and Shannon Elizabeth), Taylor (Taylor Lautner and Taylor Swift), Tracy (Tracy Morgan and Tracy Chapman), Jordan (Jordan Knight and Jordan Pruitt), and Hayden (Hayden Christensen and Hayden Panettiere). According to the Social Security Administration, Jayden has been the most popular unisex name for boys since 2008 and Madison has been the most popular unisex name for girls since 2000 in the United States. Prior to Jayden, Logan was the most popular unisex name for boys and prior to Madison, Alexis was the most popular unisex name for girls.\nCommon unisex names in English speaking countries include: Addison, Adrian, Ainsley, Alex, Alexis, Angel, Arden, Ashley, Aubrey, Avery, Bailey, Beverly, Blair, Brett, Cameron, Casey, Cassidy, Chance, Chase, Cherokee, Cody (Codi), Cory (Corey, Cori), Courtney, Dakota, Dale, Dana, Darby, Darcy, Devon (Devin), Dominique, Drew, Dylan, Elliott (Eliot), Ellis, Emerson (Emmerson), Emery, Evelyn, Finley, Fran, Gale (Gail), Grayson (Greyson), Hadley, Harlow, Harper, Hayden, Hayley, Hillary, Hollis, Hunter, Iman, Jamie, Jayden (Jaden, Jaiden), Jocelyn, Jordan, Joyce, Kai, Keegan, Kelly, Kelsey, Kendall, Kennedy, Kim, Kimberly (Kimberley), Lee (Leigh), Leslie (Lesley), Lindsay (Lindsey), Logan, London, Luca, Lynn (Lin), Mackenzie, Madison, Marlowe, Meredith, Micah, Morgan, Murphy, Noel (Noelle), Noor, Parker, Paris, Peyton (Payton), Phoenix, Quinn, Randy, Reese, Reilly (Riley), Remy, River, Robin, Rory, Rowan, Ryan, Sage, Sawyer, Shannon, Shelby, Shirley, Sheridan, Shiloh, Sidney (Sydney), Sky, Skyler (Skylar), Stacy (Stacey), Teagan (Taegan), Terry, Taylor, Tracy (Tracey), Vivian, and Whitney.\nMany popular nicknames are unisex. Some nicknames, such as Alex and Pat, have become popular as given names in their own right. The following list of unisex nicknames are most commonly seen in English-speaking countries such as Canada, the United States, Australia, South Africa, and the United Kingdom.\n- Alex - Alexander, Alexandra, Alexis, Alexandria, Alexa\n- Andi, Andie, Andy - Andrea, Andre, Andrew\n- Ash - Asher, Ashley, Ashlyn, Ashton\n- Berni, Bernie, Berny - Berenice, Bernard, Bernadette\n- Berti, Bertie, Berty - Albert, Alberta, Alberto, Robert, Roberta, Roberto\n- Bobbi, Bobbie, Bobby - Robert, Roberta, Roberto\n- Cas - Casper, Cassandra, Cassian, Cassidy, Castiel\n- Cassi, Cassie, Cassy - Casper, Cassandra, Cassian, Cassidy\n- Charli, Charlie, Charly - Charlene, Charles, Charlotte\n- Chris - Christian, Christine, Christina, Christoph, Christopher\n- Christi, Christie, Christy - Christine, Christina, Christopher\n- Dale - Dale\n- Danni, Dannie, Danny - Daniel, Danielle\n- Ed, Eddi, Eddie, Eddy - Edith, Edmund, Edward, Edwin, Edwina\n- Fran - Frances, Francis, Francesca, Francesco, Francine\n- Franki, Frankie, Franky - Frances, Francis, Francesca, Francesco, Francine, Frank, Franklin\n- Franni, Frannie, Franny - Frances, Francis, Francesca, Francesco, Francine\n- Freddi, Freddie, Freddy - Fred, Frederick, Frederica\n- Gabbi, Gabbie, Gabby - Gabriel, Gabriella, Gabrielle\n- Georgie - George, Georgeanna, Georgette, Georgia, Georgina\n- Izzi, Izzie, Izzy - Isaac, Isabel, Isabella, Isabelle, Isidore, Isolde, Elizabeth\n- Jacki, Jackie, Jacky - Jack, Jackson, Jacqueline, John\n- Jay - Jacob, James, Jamie, Jane, Jayden, Jaeden\n- Jess - Jesse, Jessica\n- Jerri, Jerrie, Jerry - Gerald, Geraldine, Gerard, Jeremiah, Jeremy, Jerome\n- Joey - Joanna, Joanne, Joseph, Josephine\n- Joss - Jocelyn, Joseph, Josiah\n- Kel - Kelly, Kelsey\n- Kris - Kristin, Kristina, Kristine, Kristopher\n- Leslie - Lester\n- Liv - Olive, Oliver, Olivia\n- Lou - Lewis, Louis, Louise, Lucas\n- Louie - Louis, Louise\n- Maddi, Maddie, Maddy - Madeline, Madison\n- Mandi, Mandie, Mandy - Amanda, Amandus, Mandel\n- Manni, Mannie, Manny - Emanuel, Emmanuel, Emmanuelle, Manfred\n- Matti, Mattie, Matty - Mathilda, Matilda, Matthew\n- Max - Maximilian, Maximus, Maxine, Maxwell\n- Mel - Melanie, Melinda, Melissa, Melody, Melvin, Melina\n- Micki, Mickie, Mickey, Micky- Michael, Michaela, Michelle, Mikayla\n- Nat - Nathanael, Natalia, Nathalie, Natasha, Nathan, Nathaniel, Natalie\n- Nicki, Nickie, Nicky - Nicholas, Nicola, Nicole, Nicolette, Nikita\n- Oli, Olli, Ollie, Olly - Olive, Oliver, Olivia\n- Pat - Patricia, Patrick\n- Patti, Pattie, Patty - Patricia, Patrick\n- Robbi, Robbie, Robby - Robert, Roberta, Roberto, Robin\n- Ronni, Ronnie, Ronny - Ronald, Veronica\n- Sacha, Sascha, Sasha - Alexander, Alexandra\n- Sal - Sally, Salvador\n- Sam - Samson, Samuel, Samantha\n- Sammi, Sammie, Sammy - Samson, Samuel, Samantha\n- Sandi, Sandie, Sandy - Alexander, Alexandra\n- Shelli, Shellie, Shelly - Michelle, Sheldon, Shelton\n- Stevie - Stephanie, Stephen, Steven\n- Terri, Terrie, Terry - Terence, Teresa, Theresa\n- Theo - Theobald, Theodora, Theodore, Theodoros\n- Toni, Tonie, Tony - Anthony, Antonio, Antonia\n- Val - Valentina, Valentine, Valentino, Valerie\n- Vic - Vicky, Victor, Victoria\n- Viv - Vivian, Viviana, Vivien, Vivienne\nFinnish law bans giving \"female child a male name and male child a female name\" among other restrictions. Some ambiguous names do exist, which have been given to children of both sexes. A partial list includes: Aala, Aale, Aali, Aalo, Airut, Aleksa, Alvi, Ami, Ara, Ariel, Asla, Dana, Dara, Eedi, Eelia, Eeri, Eeti, Eka, Ellis, Emili, Ensi, Ervi, Essa, Hami, Hani, Heile, Heine, Helgi, Helle, Hille, Ila, Ille, Ilo, Jessi, Jo, Juno, Kaari, Kaiho, Kara, Karli, Karo, Kullero, Lahja, Lei, Lemmi, Lumo, Mara, Margo, Marin, Marjus, Mietti, Mille, Miska, Mitja, Muisto, Nevin, Niika, Niki, Nikita, Nikola, Nilla, Noa, Noe, Noel, Oma, Orla, Peeta, Rani, Reine, Reita, Rene, Sana, Sani, Sasa, Sasha, Sassa, Seri, Sire, Sirius, Soini, Soma, Sävel, Tiera, Toive, Vanja, Varma, Veini, Vendi, Venni and Vilka. Many of these names are rare, foreign or neologism, established names tend to be strongly sex-specific. Notably, a class of names that are derived from nature can be often used for either sex, for example: Aalto (wave), Halla (frost), Lumi (snow), Paju (willow), Ruska (fall colors), and Valo (light). Similarly, there are some (sometimes archaic) adjectives which carry no strong gender connotations, like Kaino (timid), Vieno (calm) or Lahja (a gift).\nPopular unisex names of French origin include Camille, Claude, and Dominique. There are also pairs of masculine and feminine names that have slightly different spelling but identical pronunciation, such as André / Andrée, Frédéric / Frédérique or Gabriel / Gabrielle. In France and French-speaking countries, it can happen for people to have a combination of both masculine and feminine given names, but most of these include \"Marie\", such as Jean-Marie, Marie-Jean, Marie-Pierre. Marie was a unisex name in medieval times; it is nowadays only female except for its presence in compound names. Notable examples of people with a combination of masculine and feminine given names are Jean-Marie Le Pen (male), Marie-Jean Hérault de Séchelles (male), Marie-Pierre Kœnig (male), and Marie-Pierre Leray (female).\nEuropean royals often bear the name Marie, the French form of Maria, in their names. Prince Amedeo of Belgium, Archduke of Austria-Este (Amedeo Marie Joseph Carl Pierre Philippe Paola Marcus), Prince Jean of Luxembourg (Jean Félix Marie Guillaume), and Jean, Grand Duke of Luxembourg (Jean Benoît Guillaume Robert Antoine Louis Marie Adolphe Marc) are examples of male royals who bear Marie in their names.\nIn the past, German law required parents to give their child a sex-specific name. This is no longer true, since the Federal Constitutional Court of Germany held in 2008 that there is no obligation that a name has to be sex-specific, even if it is the only one. The custom to add a second name which matches the child's legal sex is no longer required. Still unisex names of German origin are rare, most of them being nicknames rather than formal names. Examples for unisex names derived from French: Pascal (sometimes as Pascale) or Simone (pronounced like Simon in German). Other examples: Eike, Gustl, Toni, Kai.\nMany of the modern Hebrew names are unisex. A few popular examples are Gal, Tal, Noam and Daniel (which is unisex only as a modern name).\nUnisex names are illegal in Iceland (the given name, Blær the only known legal exception). The Icelandic Naming Committee (ice. Mannanafnanefnd) has preapproved male and female lists.\nAdditionally traditional patronymic (or rarely matronymic or both) Icelandic last names (by law) can't be unisex. The suffix of the last name -dóttir (e. daughter) gives away the female sex. Males use the suffix -son (rare exceptions for foreign females; when using husbands last name as a family name; family names are in general illegal with few exceptions). Given names are also clearly masculine or feminine (to Icelanders) and linguistic gender has to match the gender identity of the person.\nAs of 2012[update], the law has been successfully challenged once, for the given male name Blær (transliterated Blaer) allowing for that one exceptionally used for females. The Icelandic Naming Committee had for 14 years rejected a girl to have her registered as Blaer in the national census, keeping her registered with the default given name stelpa (e. girl) - the name was not on the list of about 1,853 approved female names. A lower court deemed the name additionally legal for females and the state decided not to use its right to appeal.\nFew exceptions apply for linguistic gender such as the traditional name Sturla, linguistically feminine, from medieval history always applies to males and Ilmur (e. fragrance or odour), linguistically masculine, must apply to females.\nMany Indian names become unisex when written with Latin characters because of the limitations of transliteration. The spellings Chandra and Krishna, for example, are transliterations of both the masculine and feminine versions of those names. In Indian languages, the final a's of these names are different letters with different pronunciations, so there is no ambiguity. However, when they are seen (and usually, spoken) by someone unfamiliar with Indian languages, they become sexually ambiguous. Other Indian names, such as Ananda, are exclusively or nearly exclusively masculine in India, but because of their a ending, are assumed to be feminine in Anglophone societies. Many unisex names in India are obvious and are never ridiculed. For instance Nehal, Sonal, Snehal, Niral, Pranjal and Anmol are used commonly to name baby boys or girls in western states of India such as Gujarat. Similarly, names like Kajal,Sujal, Viral, Harshal, Deepal, Bobby, Mrinal, Jyoti, Shakti, Kiran, Lucky, Ashwini, Shashi, Malhar, Umang, Shubham and Anupam are also very common sex-neutral names or unisex names in India. Most Punjabi Sikh first names such as \"Sandeep, Gurdeep, Kuldeep ,Mandeep\", \"Surjeet, Gurjeet, Kuljeet, Harjeet, Manjeet\", \"Harpreet, Gurpreet, Jaspreet, Kulpreet, Manpreet\", \"Prabhjot, Harjot, Gurjot, Jasjot\" and \"Sukhjinder, Bhupinder, Jasbinder, Parminder, Kulvinder, Harjinder, Ranjodh, Sheeraz, Hardeep, Kirendeep, Sukhdeep, Govindpal, Encarl, Rajan\" are unisex names and equally commonly given to either sex. Also, names derived from Dari Persian and Arabic, but not used among native speakers of those languages, are common among South Asian Muslims. Since Persian doesn't assign genders to inanimate nouns, some of these names are gender-neutral, for example: Roshan, Parveen, and Insaaf.\nUntil 2012 it was illegal to give unisex names to children.\nCommon Italian boys' names, such as Nicola or Luca, are assumed to be feminine in English, due to the 'a' termination. This also happens to several masculine names ending with 'e', like Simone, Gabriele, Michele, Davide or Daniele.\nThe name \"Andrea\" in Italy is a male name bit it may be used, even if it rarely happens.\nDespite there being only a small number of Japanese unisex names in use, unisex names are widely popular. Many high-profile Japanese celebrities such as Hikaru Utada, Jun Matsumoto, Ryo Nishikido, Tomomi Kahala, Harumi Nemoto, Izumi Sakai, and Shizuka Arakawa have unisex names.\n- Ryou (Ryoo, Ryō, Ryota)\n- Shou (Shoo, Shō)\n- Yuu (Yu, Yū, Yuuya, Yuna)\n- Yuuki (Yuki, Yūki)\n- Yoshi (Yoshie, Yoshio)\nUnisex names may also be used as nicknames. For example, a man named Ryounosuke and a woman named Ryouko may both use the unisex name Ryou as a nickname.\nNames that end with an i are considered unisex in Brazil. They tend to be Native Brazilian Indian names in origin, such as Araci, Jaci, Darci, Ubirani, but names from other cultures are now being absorbed, such as Remy, Wendy, and Eddy. Names that end with ir and mar tend to be unisex also, such as Nadir, Aldenir, Dagmar and Niomar - though in these cases there are some exceptions.\nCommon Russian boys' names, such as Nikita and Misha (short for Mikhail), are assumed to be feminine in English, due to the 'a' termination, which is actually common in diminutive masculine forms. However, the 'a' termination does hold true for other Russian contexts, as the letter 'a' is appended to all Russian female last names (Ivanov's mother, wife, and daughter all have last name Ivanova; yet any son born out of wedlock to an Ivanova defaults back to last name Ivanov), and nearly all Russian feminine first names end in 'a' (or 'ya', a distinct letter in the Cyrillic alphabet). Also, nicknames (shortened versions of names) can be sex-ambiguous: Sasha/Shura (Alexandr or Alexandra), Zhenya (Yevgeniy or Yevgeniya), Valya (Valentin or Valentina). In all cases a noun ending in -a or -ya is declined as if it were feminine no matter the actual gender.\nIn Spain unisex names are extremely rare. In Valencia and Catalonia though, the name Pau (Paul in Catalan) was used both for boys and girls from the mid-70s. María, an originally feminine name is used for males as middle name, very commonly after José (e.g., José María). José is used for females preceded by María (María José).\nThere are many Turkish names which are unisex. These names are almost always pure Turkish names (i.e. not Turkified Arabic names that have an Islamic connotation) that derive from Turkish words. These names may either be modern names or be derived from Turkic mythology. Among the common examples of the many unisex names in Turkey include, Aytaç, Ayhan, Bilge, Cemre, Derya, Deniz, Evren, Evrim, Göksel, Gökçe, Özgür, Turhan, Toprak, Yüksel or Yücel. Some Persian-derived Turkish names, like Can and Cihan, are also unisex, as are even a few Arabic-derived names, like İhsan and Nur.\nAmong modern Vietnamese names, unisex names are very popular. Vietnamese tend to distinguish unisex names by middle names (for example Quốc Khánh is a male name and Ngân Khánh is a female name). In many cases, a male could have a female name and vice versa. Popular examples of unisex names in Vietnam are: Anh (beautiful or outstanding), An (safe and sound), Hà (river), Khánh (joy or virtue), Linh (divinity, essence, or spirit), or Tú (star), etc.\n- \"Rory and Logan: Getting Serious\". Crushable. Retrieved 23 June 2012.\n- Jayden at BehindtheName.com\n- Madison at BehindtheName.com\n- Logan at BehindtheName.com\n- Alexis at BehindtheName.com\n- \"FINLEX ® - Ajantasainen lainsäädäntö: 9.8.1985/694\" (in Finnish). Finlex.fi. Retrieved 2013-09-29.\n- \"Lapsesta Ruu tai Sirius? Sukupuolineutraaleista nimistä tuli buumi | Helsingin Uutiset\" (in Finnish). Helsinginuutiset.fi. Retrieved 2013-09-29.\n- French Unisex Names at About.com\n- French First Names at About.com\n- \"Oh no, you can't name your baby THAT!\" CNN.com\n- Flippo, Hyde \"The Germany Way\" Published by McGraw-Hill (1996), Pages 96-97\n- BVerfG, 1 BvR 576/07 vom 5.12.2008, paragraph 16\n- \"Name Law and Gender in Iceland\" (PDF). UCLA Center for the Study of Women. 9 June 2009. Retrieved September 7, 2014.\n- \"Icelandic girl Blaer wins right to use given name\". BBC. 31 January 2013. Retrieved 7 September 2014.\n- Sikh Names (SikhNames.com) Sikh Names, Meanings & Pronunciation"

"What's in a name, you ask? Surely not \"vowels\" in the case of a newborn boy from Carmen, Cotabato who was given an unusual name that is difficult to pronounce and spell.\nInterviewed in Mark Salazar's report on \"24 Oras,\" the child's grandfather, Raugyl Ferolin Estrera, decided to name the baby boy as Ghlynnyl Hylhyr Yzzyghyl Mampuan Buscato.\nEven the personnel who processed the baby's birth certificate had to reprint the document because they committed errors in spelling his name, Estrera shared.\nTo make things easier for everybody, Estrera vowed to give his grandson the much simpler yet equally unusual nickname of \"Consonant,\" owing to the absence of regular vowels in the boy's real name.\nThe boy's name, however, is not actually vowel-less. The letter Y, though commonly regarded as a consonant, is also considered a special vowel as it can represent vowel sounds depending on its position and the letters surrounding it in a word.\nEstrera explained that his grandchild's name, \"Ghlynnyl Hylhyr Yzzyghyl\" was formed by combining a few letters from his name as well as the names of the child's father, mother, and grandmother.\nEstrera further said a few letters from baby Consonant's name was also derived from his niece's name.\n\"If I will give him a name, it should be something of value for our family. The child's name shouldn't be made up,\" Estrera said in Filipino, when asked about his inspiration for baby Consonant's name.\nOnce baby Consonant starts to learn reading and writing, Estrera said they will teach him how to spell his name as well as tell him about its origin.\n\"At an early age, we will teach him how to write his name. We will explain the origin of his name so that he will have an idea. The child will know the importance of his name,\" Estrera said. -Consuelo Marquez/MDM, GMA News"

"Definitions for \"Cousin\"\nOne collaterally related more remotely than a brother or sister; especially, the son or daughter of an uncle or aunt.\nIn colonial times, it most often meant nephew or niece. In the broader context, it could also mean any familial relationship, blood or otherwise,( except father, mother, brother, sister), or the contemporary meaning of a child of one's aunt or uncle. Modern usage includes qualifiers such as first, second, third, and once removed, twice removed, etc. First cousin is what most people commonly call their cousins, that is an aunt's or uncle's child. Second cousin is a child of the first cousin, as is a first cousin once removed. Similarly, a first cousin twice removed and a third cousin denote the same member of the family--a first cousin's grandchild.\nthe child of your aunt or uncle\nSomeone who has some autistic spectrum characteristics to the extent that he/she can identify with autistics even if he or she does not have a formal diagnosis. People with Schizoid Personality Disorder, Obsessive Compulsive Disorder (OCD), Tourette Syndrome (TS), and sometimes Attention Deficit Disorder (ADD/ADHD), are considered cousins. See also: Autistics and Cousins (AC).\nOne chain letter is the cousin of another if they are both members of some clade under discussion, but are members of different major sub-clades. Usually the letters are understood to circulate at about the same time.\na freshman at Howard University majoring in pre-med biology in the honors program of the College of Arts and Sciences\na pilot with a commerical airline and my Dad is a private pilot, has a commercial licence and is a PPL instructor\nA title formerly given by a king to a nobleman, particularly to those of the council. In English writs, etc., issued by the crown, it signifies any earl.\nUsually the term used to describe the anchor player on a team that had a chance to \"stick\" a teammate with a beer frame, but did not strike. The anchor is said to be a \"cousin\" of the other player. Also, the name of the pin that is hidden in a spare cluster; i.e., the 8 in the 2-8, or the 9 in the 3-9; a \"sleeper\".\na famous actor/singer married to an also famous actress/singer\nSenses whose hyponyms bear a specific relation to each other."

"A symbol identifying a genetic lineage as a paragroup of a specified haplogroup\nStar (game theory), the value given to the game where both players have only the option of moving to the zero game\nIn linguistics, a symbol that prefixes a word or phrase that, in historical linguistics, is a reconstructed form for which no actual examples have been found; and in linguistics of a modern language (see: synchronic linguistics), is judged ungrammatical\nThe symbol is used to refer a reader to a footnote\nThe symbol is used to refer a reader to an endnote\nThe following characters had significant roles in the American television comedy series Malcolm in the Middle, which was originally televised from 2000–2006 on the Fox Network.\nOriginally there were four brothers (although Malcolm's oldest brother attended a military school away from home, so Malcolm was still the middle sibling left at home). A fifth son was introduced in the show's fourth season, a boy named Jamie. The boys are, from eldest to youngest: Francis, Reese, Malcolm, Dewey, and Jamie. In the final episode, Lois discovered she was pregnant with a sixth child. In the third season, Francis travels home (to celebrate his father's birthday) with an Alaskan girl named Piama, and reveals that they are married.\nDuring the first season, the writers decided to keep the family's last name a mystery. In the fifth season episode \"Reese Joins the Army (1)\", Reese uses a fake ID by the name of \"Jetson\" to lie about his age. In the series finale, \"Graduation\", Francis' employee ID reads \"Nolastname\" (or \"No Last Name\", a joke referring to the fact that the family name was never spoken aloud). In the same episode when Malcolm was introduced to give the graduation speech, the speaker announces Malcolm's name, but microphone feedback makes his surname inaudible, even though he does appear to mouth the phrase \"No last name\".\nFrancis is a name that has many derivatives in most European languages. The female version of the name in English is Frances, and (less commonly) Francine. (For most speakers, Francis and Frances are homophones or near homophones; a popular mnemonic for the spelling is \"i for him and e for her\".) The name Frank is a common diminutive for Francis and Fanny for Frances.\nIn Spanish, Francisco is usually used under the forms Paco, Paquito, Curro, Fran or Pancho (in Latin America). The feminine Francisca is mostly used as Paqui or Paquita.\nFrancesco (\"the Frenchman\") was the name given to Saint Francis of Assisi (baptized Giovanni) by his francophilefather, celebrating his trade with French merchants. Due to the renown of the saint, this Italian name became widespread in Western Europe during the Middle Ages in different versions (Francisco, François, etc.). However, it was not regularly used in Britain until the 16th century as Francis."

"It doesn't look much like my last name, Manis, but when you pronounce it it's pretty close. A bully who shall remain (ironically, given the topic of this post) nameless started using it. Before long, my football coaches picked up on it and were yelling it at me at practice after practice. No, I never liked it.\nNames are powerful things, more powerful than we realize. I got to thinking about this during a message from our teaching pastor Sunday morning, where he was talking about how Jesus gave his disciple Simon a new name, Peter. More on that in Part 2 (to be posted tomorrow). But in the wake of that talk, I thought about how often we see the power of the name. For example,\n- In Romeo and Juliet, the names of the two young lovers' families - Montague and Capulet - drive a wedge between them that they could never overcome. From the balcony Juliet tried to deny it (\"What's in a name? That which we call a rose by any other name would smell as sweet\" - Act II, Scene II), but by the end of the play, we saw that there was indeed a lot in a name.\n- While not universal, it's customary in our society for women to take the name of their husband when they get married. This has rich symbolism, because if two are going to become one, having a common name says so to the world.\n- In Ethiopia (at least the part I visited), a child's last name is the name of his father. So, if I lived there, instead of Donnie Manis, my name would be Donnie TJ. The name identifies one very strongly with the father.\n- In a recent episode of Revolution, the former President of a vast empire called the Monroe Republic finds his 25-year-old son in a forgotten hole-of-a-town, and reveals that he is his father. The son is not impressed until he reveals his name - Sebastian Monroe. Because of the name, which was well known, the son's whole attitude was changed instantly.\n- When Moses encountered the burning bush and God was calling him to lead his people out of slavery, Moses insisted on being given a name. The name he received, YHWH, was basically the same as the Hebrew for \"I am.\" The most powerful name ever given.\nThroughout history, in popular culture, in just about every society, the name has extraordinary significance. Your name is who you are. It matters. And that's why some name changes in the Bible tell us a lot about what God was doing in the lives of his people. People like Abram. Jacob. Simon. Daniel. Saul.\nComing tomorrow: Name changes through history - why?"

"Shakespeare’s play “Romeo and Juliet,” centers on two young people – one each from feuding families. At one point Juliet muses that Romeo’s last name doesn’t make him any less a wonderful person. She says, “A rose by any other name would smell as sweet.” The meaning is that the names of things do not affect what they really are. While it is true that “Montague” is neither good or evil in itself, any more than “Capulet” – it is also true that many times a name or a title describes exactly the sort of person who carries it. While a “Republican” may be either a liberal or a conservative, a “Christian” ought to thoroughly honor Christ, according to the narrow confines of the Word of God. There are no wide-ranging liberal and conservative Christians\nTonight I intend, the Lord willing, to begin a series of messages looking at titles which have been applied to God’s people. We will start with those which we find in the Bible, but eventually we will move into historical names. My intention is three fold – the first is simply educational. But my second goal is to show that quite often we fall short of what these titles convey. So my third point will be – here in this title is what we should strive to become for the glory of our Saviour.\nTonight we will start with the term “disciple.” It might be argued there are better places to start. One might think we should begin by looking at the word “Christian” – but “Christian” is rather rare title in the Word of God. Someone else might suggest “saint,” or something else, and they might be right. But having to start somewhere, I have chosen “disciple” because during the ministry of Christ and in the Book of Acts, it was the Holy Spirit’s favorite term. Did I mention when we were looking at Matthew 27 that the word “saint” is found only once in the gospels? And the title “Christian” cannot be found in any of the four gospels. But the word “disciple” or “disciples” is found 226 times in Matthew, Mark, Luke, John and Acts. Just the sheer number tells me to start with this word. Whether or not it is the most important, we’ll just have to the let the Spirit teach us one way or the other.\nAre you one of the Lord’s disciples? Do you know what “discipleship” really entails?\n“Go ye therefore and teach all nations.”\nWhen we looked at the great commission a couple months ago, did you notice that we were NOT ordered to make people into “Christians?” Never have we been commanded to turn “sinners” into “saints.” And as much as it might grieve you or me – while we have orders to baptize people – we have no scriptures telling us to make people into “Baptists.” That isn’t to say we shouldn’t long to see people become Christians, saints or even Baptists. But our commission is to make “disciples.” The word translated “disciple” is “mathetes” (math-ay-tes’). In Matthew 28:19 – “Go ye therefore and teach all nations” – “teach” is “matheteuo” (math-ayt-yoo’-o).’ Our commission is to go into all the world and to “make disciples.”\nAnd what is the literal meaning of that Greek word? At its most basic meaning, a disciple is a student, a learner, someone who is being taught. Under the authority of Christ (Matthew 28:18), the Lord’s church is commissioned to teach God’s word. It is our task to follow the leadership of the Holy Spirit in looking for people willing to be taught. But wait a minute – that makes THOSE people disciples, but what about us? The answer is in the context of that great commission – “Then the eleven disciples went away into Galilee, into a mountain where Jesus had appoint them. And when they saw him, they worshipped him…. And Jesus came and spake unto then saying, All power is given unto me in heaven and in earth. Go ye therefore, and (disciple) all nations.” Who were to disciple the nations? Those who were already Jesus’ disciples.\nI will come back to this, but it’s important to realize that true disciples are more than just students. Judas was a disciple in one sense, in other ways he was not. And there were disciples in John 6 who forsook the Lord. Were they ever really disciples? Joseph of Arimathea was a secret disciple – something which is definitely not ideal. Am I a true disciple of Christ? Are you?\nDiscipleship involves a special relationship.\nLet’s say that I have been pastor of this church for 25 years – and, lo, that is the case. Let’s say that some of the members of this assembly came to know Christ under my ministry. As new born babes in Christ, they joined this church, and this has been their only church. It might be possible that much of what they know of the Bible they learned from me. I have preached and taught a great many messages in 25 years – more than 5,000. But I hope that not one of you would ever say that you are a “disciple” of Kenneth David Oldfield. The term “disciple” suggests a very special relationship which goes beyond teacher and student, or pastor and church member.\nMany centuries ago the Old Testament was translated into the Greek language by seventy Jewish scholars. That translation is called the “Septuagint” – and it is commonly denoted by the Roman numerals “LXX.” Those men did not use the Greek word “disciple” in the Septuagint, even though it had been commonly used in Greek literature since before 500 BC. But just because the term isn’t found, we do find disciples in the Old Testament – in a limited sense. Perhaps they began with Elijah, but clearly by the time of Elisha, there were schools of the prophets. There are several accounts of visits, lessons and even miracles among the students of those schools. Would any of his students ever call himself “a disciple of Elisha”? I don’t know. But there was one student who stands out from all the others in the relationship he had with his master. One cannot find a more faithful illustration of a disciple than Elisha was of Elijah. Elisha refused to leave his teacher – he was a servant, student, aide and successor to his Master.\nBut Elisha and Elijah are not only teachers and students in the Old Testament. Isaiah apparently had his school and his students. Isaiah 8:13 – “Sanctify the LORD of hosts himself; and let him be your fear, and let him be your dread. And he shall be for a sanctuary; but for a stone of stumbling and for a rock of offence to both the houses of Israel, for a gin and for a snare to the inhabitants of Jerusalem. And many among them shall stumble, and fall, and be broken, and be snared, and be taken. Bind up the testimony, seal the law among my disciples. And I will wait upon the LORD, that hideth his face from the house of Jacob, and I will look for him.” For some reason the Septuagint didn’t translate Isaiah 8:16 with the same Greek word. But the Hebrew has exactly the same meaning – learner, student.\nWhat did the Greek word “disciple” mean to the Greeks who used that word? To be honest it meant different things to different people. But in its highest form, discipleship referred to a surrender to one’s teacher as his master. In Greek literature there are the disciples of Socrates, Plato, Pythagorus and others. The disciples of these people were committed to following their leader, emulating his life, learning what he had to say, and then passing those teachings on to others. To these people “discipleship” was much more than just the reception of information – studenthood. It meant imitating the teacher’s life, ingesting his values and ideas and then reproducing his instructions. IF this is the true definition of a “Christian disciple” are you a disciple of Christ?\nIn the New Testament we see a variety of disciples.\nSometimes we see the Greek kind of discipleship spilling over into Jewish society. Is this the kind of disciple which followed John the Baptist? Not all of those 226 references to “disciples” in the Gospels and Acts are speaking of Jesus’ disciples. There were apparently people who chose to make John their “master.” They followed him about, learning from him, emulating him, sharing what he taught them. But then he pointed to Jesus and said, “Behold, the Lamb of God which taketh away the sin of the world.” At that point the most worthy disciples of John became disciples of Jesus. In Acts the word “disciple” continued to be applied to Johns’ disciples. Those men of Ephesus in Acts 19 were disciples of John, and yet they had probably never met him. What they claimed was to adhere to his teachings, and they went about the world spreading those teachings.\nNot only did John have disciples, but so did the Pharisees. The Pharisees were disciples and they had disciples of their own. When Christ cured a man who had been born blind, the Jews began to attack the poor man. But he kept his wits about him and availed himself quite well. John 9: 24 – “Then again called they the man that was blind, and said unto him, Give God the praise: we know that this man is a sinner. He answered and said, Whether he be a sinner or no, I know not: one thing I know, that, whereas I was blind, now I see. Then said they to him again, What did he to thee? how opened he thine eyes? He answered them, I have told you already, and ye did not hear: wherefore would ye hear it again? will ye also be his disciples? Then they reviled him, and said, Thou art his disciple; but we are Moses’ disciples.” What did they mean in saying that they were Moses’ disciples? Wasn’t it that they claimed to be obedient followers of Moses’ teachings?\nMark 2:18 – “And the disciples of John and of the Pharisees used to fast; and they come unto (Jesus) and say unto him, Why do the disciples of John and of the Pharisees fast, but thy disciples fast not?” That is an excellent question – at least in one aspect – Notice that these disciples were not hearers only – not students only – they imbibed and practiced what their masters had taught them. Luke 11:1 – “It came to pass that, as (Jesus) was praying in a certain place, when he ceased, one of his disciples said unto him, Lord, teach us to pray, as John also taught his disciples.” In John 3 we see the disciples of John quarreling with some of the disciples of the Jews. Why were they quarreling? Because they were more than mere students. And why was Saul of Tarsus such a dangerous enemy to early Christianity? It was because he was a disciple of Gamaliel – the Pharisee. Paul had received the lessons of his master, and at some point decided defend them by attacking the disciples of Christ Jesus. To be a disciple is more than just to be a student of the master.\nWhat does the Bible say is meant by becoming a disciple of Christ?\nSometimes, it isn’t what is said, but what the Bible implies. For example what is meant by the words of Matthew 10:42 – “And whosoever shall give drink unto one these little ones a cup of cold water only in the name of a disciple, verily I say unto you shall in no wise lose his reward.” Doesn’t that suggest that the one giving this cup of water is doing so as a representative of Christ. At least in this verse, he is much more than a mere student of the Lord. And what is implied in the next verse – Matthew 11:1 – “And it came to pass, when Jesus had made an end of commanding his twelve disciples…..” At least in this verse the twelve are not students – they are servants and representatives of Christ.\nDespite the basic meaning of the word, “disciple” means much more than a mere student. But the critical question is – does it mean anything more TO US? Am I misreading Matthew 16:24 when I say that to be a disciple is to be a selfless follower of Christ? “Then said Jesus unto his disciples, If any man will come after me, let him deny himself, and take up his cross, and follow me.” Isn’t Jesus saying that disciples deny themselves and follow Christ, bearing their cross?\nIn John 8, the Lord was teaching various points of doctrine to people of varying degrees of discipleship. In verse 31 – “Then said Jesus to those Jews which believed on him, if you continue in my word, then are ye my disciples indeed. And ye shall know the truth, and the truth shall make you free.” Is there any special significance to the word “continue” – “if you continue in my word you are disciples?” Doesn’t it mean more than simply to mentally learn the truth? Doesn’t it imply learning, abiding and living in that truth? Doesn’t it involve making that truth a part of one’s life? Based on John 8:31 are you a disciple of Christ?\nWhat would I mean if I referred to someone as a disciple of Charles Darwin? Wouldn’t I mean that the person not only believed what Darwin taught, but that he was a defender and teacher? A disciple of Lenin, is more than a citizen of Russia – he is a dyed in the wool communist. He would fight to make converts to his position. Are you a dyed in the wool follower of Christ?\nWhat is the instruction of John 15? “I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing. If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned. If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you. Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples.” Doesn’t our Master tell us that unless we are bearing fruit, we are not really His disciples?\nDoes I Corinthians 1:9 shed light on the question of discipleship? “God is faithful, by whom ye were called unto the fellowship of his Son Jesus Christ our Lord.” What is meant by “fellowship”? If I am not mistaken it is more than sitting in class, learning a few Bible doctrines. And although we see some pretended and short term disciples of Christ, those who were disciples indeed, were invited into that relationship – “by whom ye were called.” Called unto what? Fellowship, communion, friendship, instruction, stewardship and service. And never forget that we are talking about disciples of God’s Son “Jesus Christ our LORD” and Master.\nPhilippians 3:10 also uses that same word “koinonia” – “fellowship.” “But what things were gain to me, those I counted loss for Christ. Yea doubtless, and I count all things but loss for the excellency of the knowledge of Christ Jesus my Lord: for whom I have suffered the loss of all things, and do count them but dung, that I may win Christ, And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: That I may know him, and the power of his resurrection, and the fellowship of his sufferings, being made conformable unto his death; If by any means I might attain unto the resurrection of the dead. Not as though I had already attained, either were already perfect: but I follow after, if that I may apprehend that for which also I am apprehended of Christ Jesus. Brethren, I count not myself to have apprehended: but this one thing I do, forgetting those things which are behind, and reaching forth unto those things which are before, I press toward the mark for the prize of the high calling of God in Christ Jesus.” If there has ever been a true disciple of Christ, Paul must stand among them. Could we say that this paragraph from Philippians 3 is the motto of the true disciple? Then what about I Corinthians 11:1 – remembering that disciples – disciple. Paul says, “Be ye followers of me, even as I also am of Christ.” To be a disciple is to be a follower as well as a learner, because our Divine Teacher, our Master, isn’t seated at a desk or standing behind a lectern; He is on the go, working.\nAnd this business of following naturally involves some degree of sacrifice. Can someone be a true disciple of Christ without the involvement of sacrifice? What did the Greek word “disciple” mean to the Greeks who used that word? If someone became a disciple of Plato, then it might mean the loss of his family and his former life. It was more than just learning the principles of Plato, it was becoming a new Plato. Discipleship meant imitating the teacher’s life, ingesting his values and reproducing his instructions.\nWhat does Luke 14:33 say? “Whosoever he be of you that forsaketh not all that he hath, he cannot be my disciple.” That statement came after Christ said we may have to forsake our parents in becoming His disciples. What was the Lord saying in Matthew 12? “And he stretched forth his hand toward his disciples, and said, Behold my mother and my brethren! For whosoever shall do the will of my Father which is in heaven, the same is my brother, and sister, and mother.” Doesn’t the Lord imply that the relationship of a disciple to Christ is greater and more intimate than that of a child to his natural parents? Is this the kind of discipleship that we have? In order to be a disciple of Christ, according to the New Testament pattern, there must be a willingness to forsake everything of earthly value – if it stands between us and our Master. “But what things were gain to me, those I counted loss for Christ.”\nThe Bible has high standards for Christ’s disciples. Attending the house of God and learning a handful of Biblical doctrines does not make a person a true disciple. So again I ask – Am I disciple of Christ? I mean – Are you a disciple of Christ? And according to the Great Commission, isn’t discipleship a part of our core responsibilities?"

"A man became a woman – and it wasn’t even Caitlyn Jenner.\nEven though English is not technically a Romance language, many of the rules apply to the usage and formation of words – including names. In French, Italian and Spanish, names ending in O are male, and names ending in A are female. In English, numerous male names are made female, by adding an A. Don becomes Donna. Robert becomes Roberta. Shawn becomes Shawna. Paul becomes Paula.\nWe all probably know several of these, but I’ve run into a few less common ones that you may not have seen. Most Dons are actually Donalds. For those who think of themselves, formally, in that way, a few have daughters named Donalda. I’ve met two.\nThe name Donald is reasonably common, at least among my Scottish relatives. The name Samuel is currently less common. I recently met a Samuela. Like Samuel, Simon tends to be a Jewish name, and fairly rare in English. I recently ran into a Simona. The less common man’s name, Roland, has the even rarer Rolanda, female equivalent.\nShakespeare is accused of creating more than 50 new words for the English language, a few out of whole cloth, but many by merging other words, or adding suffixes. He also added at least four new female names. He created the name Perdita for the daughter of Hermione in his play ‘The Winter’s Tale’ (1610). It is a Latin word, which means lost. While first produced in England, this rare name is most often found among Spanish-speaking people. Kenneth Bulmer used it as the name of an evil villainess in The Key to Irunium, and several other books in this series.\nDerived from Latin mirandus meaning “admirable, marvelous, wonderful”, the name Miranda was created by Shakespeare for the heroine in his play ‘The Tempest’ (1611), about a father and daughter stranded on an island. Modern baby-name books now say that it means ‘cute.’\nHe constructed the female name Jessica from the Jewish male name Jesse, the father of David, meaning God Exists. The female version is now taken to mean, God beholds, or God’s grace. He gave it to the daughter of Shylock, in ‘The Merchant of Venice’ (1596/1599). The original Hebrew name Yiskāh, means “foresight”, or being able to see the potential in the future.\nOlivia is a feminine given name in the English language. It is derived from Latin oliva “olive”. William Shakespeare is sometimes credited with creating it. The name was first popularized by his character in ‘The Twelfth Night’ (1601/1602), but in fact, the name occurs in England as early as the thirteenth century. In the manner of extending the olive branch, the name indicates peace, or serenity.\nAll of these names end in the feminine-indicating final letter A. Not a Chloe, or an Amber, or a Summer, or a Robyn in the bunch. What did your parents name you…. Or, what did you name your daughter?? Are there any regrets?"

"- Family and Parenting\nWhat is In a Name, How Did You Get Your Name?\nA Rose by Any Other Name\nDo you remember the lament of Juliet (William Shakespeare, Romeo and Juliet ):\n\"What's in a name? That which we call a rose\nBy any other name would smell as sweet.\"\nWould any other name really smell as sweet? Maybe yes, maybe no, what do you think?\nNames are our identifying windows to the world. Our names are our brand or logo in other words. So it is fascinating to find out why you got your name. There is always a story behind it.\nDo you know why you are so named? Does your name have a special meaning or is it just based on your parents' whim?\nIs your name Jonathan or Paul or Justine or Bernadette? Find out if the way you got your name falls under the categories below.\nHow Did You Get Your Name?\ndiscovered several reasons why people are so named. If the reason for your name\nis not in the following list, then please add it here. I would like to hear\nHere are some reasons I gathered why you are given a certain name:\n- Your name is based on the saint's feast day on the calendar. This is especially true for those who are Roman Catholics. For example if your birthday is today, you might have the name \"Betilla\" because it is St. Betilla's feast day today (Oct 20).\n- According to a friend, “the common practice in India has been to open the holy book, Gita, Bible or Quran and the first letter on that page provides the lead to choose the name of the child. In case the birth of the child is delayed for any reason, the names like Faqir (beggar) or Garib (poor) or Allah Ditta (God Given) are chosen as first and middle name”.\n- You are the junior of your parents. So you are John, Jr., or Marian, Jr. I had a classmate in college whose name and those of his siblings are: Reginald, Jr, Reginald II, Reginald III, and Reginald IV. Apparently the family either wanted to have their “brand” or are just lazy to look for another name.\n- Your name is a combination of your parents' or grandparents' names. So it might be \"Jonel\", a combination of Jonathan and Elizabeth, or \"Jumila\", combination of Justo and Milagros or “Miranella”, combination of the grandparents Miranda, Ramon, Nelson and Lagrima.\n- Your name is the diminutive form of your parents’ or a favourite relative’s name. So if your father’s name is Jose, then your name must be Joselito or if your mother’s name is Paula, then your name must be Pauline or Paulette.\n- All the names in your family start with the letters of your parents names. All the boys follow the father's name or the girls the mother's or it can be the other way around.\nSo if your parents names are Peter and Mary, then maybe your names are: Paul, Pedro, and Pistachio; or Martha, Maritess, and Marilyn; or Patricia, Peggy and Paula; or Mario, Maximo, and Medardo\n- You are the son of Sam, so your name is Samson or Williamson if you are the son of William.\n- Your name is based on the favorite actor or actress/author/singer/idol/player of your parents. So for example, you might be named Harry (Potter) or Charice (Pempengco) or Angelina (Jolie) or Barbra (Streisand) or Rafael (Nadal).\n- Your name is a combination of your parents’ favourite characters or saints or stars. So your name is “John Martin”, a combination of John Kennedy and Martin Luther King or “Marie Charles” a combination of Marie Curie and Charles Darwin.\nYour parents hope that you will turn out to be the next scientist or world leader or philosopher so you are given the name \"Einstein\" or “Galileo” or \"Indira\" or \"Corazon\" or \"Descartes\"\n“A good name is more desirable than great riches;\nto be esteemed is better than silver or gold.”\nSignificant Date or Day\n- You are born on a significant date or day, so your name is \"Millennium\" or \"Ondoy\" (typhoon here in the Philippines) or \"Katrina\" (hurricane in the USA)\nBy the Month or Day\n· You are born on a specific day of the week or month of year, so your name is \"May\" or \"Tuesday\" or \"January\" or “Friday”\n- You have American Indian parentage\nand according to myth (or practice), your name is the first thing that\nyour mother saw after giving birth to you. So your name is “Morning Star”\nor “Mountain Horse”.\nI have researched on this and according to some this is partly true, while others say that this story is just a set up for a joke. However, it is really true that American Indian names are almost always based on nature like “Silver Cloud” or “Laughing Brook”.\n- You are from Bali and you are named according to your system of names which uses only 4 names (and their variations) based on the order of birth. So your name is “Wokalayan” (or its variation) if you are 1st born, “Made” if 2nd, “Nyoman” if 3rd, and “Ketut” if 4th in line. If you are a 5th child however, then you will be “Wokalayan Balik”. “Balik” means return or again.\nYour parents use names from their profession. I actually have a friend whose name was Beta and her siblings are Alpha and Gamma. One parent (I forgot which one) is a physicist.\nI had a professor in college who named some of his children with the scientific names of some plants/animals. One daughter has the name of Eimeria (scientific name of a protozoan)\n- According to stories, people in the Philippines used to have only one name. When the Spaniards came, we were baptized and given a second name or surname. For easier identification, the beginning letters of the surname was based on location.\nSo those coming from a certain place had names beginning with a specific letter like “M” or “O”, etc. I still remember being told that somebody comes from “Dao” for example because his surname is De Leon.\n- Some English names tell of the location, like “Lancaster” or “Burroughs”.\n- Your parents stayed in some foreign country or studied some foreign language and they fell in love with some of the foreign sounding names like: Keira (Irish), Maganda (Pilipino), Aiko (Japanese), Celio (Portuguese)\nBy the Numbers\n- Your parents consulted numerology or the horoscope so your name must exhibit a certain vibration or must sum up to a specific number, etc.\nSo your name is \"John Paul Castro\" which comes up to the number 11. Number 11 is characterized by high spirituality, intuition, etc.http://www.paulsadowski.com/numbers.asp\n· Your parents were hoping for a baby girl or boy so they prepared only for girls' or boys' names. Then you turned out to be of the opposite sex (this was before the advent of ultrasound) and your parents did not bother to find another name but just changed the sex of the name. So your name was originally \"Teresita\" but you turn out to be a boy, so now you are named \"Teresito\"\nReasons, Reasons, Reasons\nThose listed above are just some of the reasons I gathered why you are given a specific name. If you know of other reasons, please add them here in the comments. Thank you!\nWhat is In a Name?\nThis is a handed down joke:\nA man angrily stopped his car and got off when it was accidentally hit by a stone thrown by a boy playing on the sidewalk. He asked for the boy’s name and the boy answered in fear, “Joking”.\nMan: “I’m asking for your name, not for the reason why you threw the stone!”\nThe man repeated his question, “what is your name?”\nBoy: “Joking, my name is Joking.”\nMan: “You must be kidding!”\nBoy: “No, that’s the name of my other brother”!\nI wish to invite you once again to please share how you or somebody you know got his/her name. Thank you!\nSome References and Articles About Names\nhttp://www.bbc.co.uk/history/familyhistory/get_started/surnames_01.shtml This is written by Paul Blake, a professional genealogy and local-history lecturer.\nhttp://visitpinas.com/a-rhose-by-any-other-name This article is written by an ex-pat about the humor in Philippine names"

"What’s in a name? Monikers alter empathy in the brain\nPosted June 29, 2017 | View original publication\nWhat’s in a name? That which we call a rose by any other name would smell as sweet.\nJuliet spoke these words in Shakespeare’s “Romeo and Juliet.” Wanting to be with her love, she attempted to cast aside the familial names of her’s and Romeo’s warring families, the Montagues and Capulets.\nBut as Juliet found later, names carry a lot of weight. In fact, new research from the University of Nebraska-Lincoln has shown that names have the power to mold empathy.\nPsychology graduate student John Kiat and Jacob Cheadle, a Husker sociologist, were able to map brain functions to show empathy is altered — for better or worse — by putting a name to a face. Because empathy is known to increase kinder behavior, understanding this experience of feeling another person’s condition from their perspective is important to building lasting social change, Kiat said.\n“If you talk about racism, sexism or classism — all these things — one of the primary drivers is a lack of empathy,” Kiat said. “Empathy is caring, and until you get enough people who care, things don’t really change. And this shows names matter.”\nEmpathy is often studied from developmental or psycho-social frames. Researchers only recently have begun to examine empathy through the functions of the brain. Kiat and Cheadle’s work is the first study in which electroencephalogram, or EEG, technology was utilized to map electrical impulses in the brain and examine the link between attentional neural responses and names, in the formation of empathy.\nUsing computer-generated faces, volunteers first were shown a resting face, then viewed the face with a grimace of pain and were asked to rate the pain they were seeing. This task was completed with 36 different faces. The experiment was repeated, but in the second series, a name was given and seen prior to the resting faces and pain expressions. When the names were added before the pictures, the neural responses changed significantly.\n“During the experiment, when we saw how their brains were responding to the named faces, we could predict almost 50 percent of participants’ empathy levels,” Kiat said.\nKiat described this as possibly being due to a strong relationship between empathy and the perceptions previously held toward different identifying labels.\n“If you know and like a Sarah and you think Sarah is tough, that may well influence the empathy you have not only for that Sarah but for other Sarahs as well,” Kiat said.\nThe study demonstrates that what drives our empathy is deeper than what we directly perceive, Kiat said.\n“Information regarding identity is important, and names clearly shift the informational bases of empathic response,” he explained.\nThe findings will be published in the July issue of NeuroImage."

"Emilia - Meaning of Emilia\n[ 3 syll. e-mi-lia, em-il-ia ] The baby girl name Emilia is pronounced eh-MIYL-Yaa (Italian, Polish, Spanish) †. Emilia has its origins in the Latin language. It is used largely in English, Hungarian, Italian, Finnish, German, Polish, Portuguese, Romanian, Scandinavian, and Spanish. It is derived from the word aemulus which is of the meaning 'imitating, rivaling'. An old form of the name is Aemilia (Latin). The name was first used by English speakers in the medieval period. It has appeared in Shakespeare's works as the name of Iago's wife in Othello (1603) and Hermione's maid in The Winter's Tale (1611).\nIn addition, Emilia is an English, Hungarian, and Italian form of the English, German, Dutch, Italian, Latin, and Spanish Amelia.\nEmilia is also a Finnish, German, Italian, Polish, Romanian, Scandinavian, and Spanish form of the English Emily.\nEmilia is the feminine equivalent of the Italian and Spanish Emiliano.\nEmilia has 14 forms that are used in English and foreign languages. English forms of Emilia include Amilia, Emelia, Emila, Emilea, Emileah, Emilya, Emilyah, Emmi (used in Finnish as well), Emmilia, and Melia. Other English variants include the contracted forms Em and Mila (used in African, Czech, Polish, Russian, Slavic, Spanish, and Swahili as well). Forms used in foreign languages include Emiliana (Italian, Portuguese, and Spanish) and Emilka (Polish).\nEmilia is popular as a baby girl name, and it is also regarded as trendy. The name has been rising in popularity since the 1980s. At the recent peak of its usage in 2018, 0.218% of baby girls were named Emilia. It had a ranking of #58 then. In 2018, out of the family of girl names directly related to Emilia, Amelia was the most popular. The name was thrice as popular as Emilia in that year.\nBaby names that sound like Emilia include Emalee, Emali, Emaly, Emanuelle, Emele, Emelee, Emeli, Emelie, Emellie, Emelly, Emely, Emilee, Emilei, Emiley, Emili, Emilie, Emillie, Emilly, Emilou, and Emily.\n† Pronunciation for Emilia: EH as in \"ebb (EH.B)\" ; M as in \"me (M.IY)\" ; IY as in \"eat (IY.T)\" ; L as in \"lay (L.EY)\" ; Y as in \"you (Y.UW)\" ; AA as in \"odd (AA.D)\""

"The sport bible says that if you’re going to use a pronoun that starts with a letter, you should be consistent in using it in the first instance.\nFor example, “I” is a pronoun.\nBut if you use “I, you” instead of “you, I”, the pronoun should be changed to “I”.\nThe word “I”, however, has a slightly different pronunciation, and that’s what makes this example particularly funny.\nI like to pronounce my name “Doe” like this, but this one is an exception.\nThis isn’t a joke, it’s a sign of respect.\nSo, I don’t have to say “you”, I just have to use the pronoun “I.\nNow that you’ve learned the difference between the pronoun you’re using and the pronoun that it should be, you might ask yourself: “Is there a more perfect pronoun than ‘I’?” It turns out there is.\nIt’s the pronoun used by the Italian poet and poet laureate Francesco Gabriele.\nGabriel is famous for his use of the pronoun “Doe”, which is a bit of a pun.\n“Gabriele” means father, and his son is the name of the daughter of the father. “\nDoes” are the nouns for women who have children, but in the 16th century, the noun for a child was also a woman.\n“Gabriele” means father, and his son is the name of the daughter of the father.\nThat makes sense, right?\nSo, Gabriella is an Italian poet.\nHe’s written poetry that deals with fatherhood and family.\nIt turns up in the works of the likes of John Steinbeck, Robert Frost, and, of course, Proust.\nSo Gabriellas use of Does, a pronoun not unlike “I,” has a bit more of an Italian flavour to it than Gabrieles, as well.\nNow, Gabriellas son, Federico, is a great poet and has his own website, so you might expect to find his name there.\nHowever, Gabielle is his real name, and it is spelled differently.\nHe was born in Sicily, and he lives in Italy, where he was raised.\nGabriele’s daughter Francesco, on the other hand, was born and raised in the United States, and so Gabrielis son, on top of having the same name, is the son of Francesco.\nIn the book The Art of Manliness, Gabiele writes about his father and his mother.\nThe son was born on August 17, 1752, and the mother was born about 18 months later.\nGabiellas father is a lawyer and a well-known man.\nFrancesco was a great man, and Gabrielli is one of the most famous poets of the 19th century.\nWhen Francesco died in 1795, Gabiole went to live with his mother in Rome.\nFrancescos son, Francesco Giovanni, was a well known man.\nHe had an enormous popularity and he wrote many great books, like L’Inferioria and Fantastica and also Romeo and Juliet.\nAnd, of the few poems that Gabrielez son wrote, he uses the name “Gabriella” to honor his father.\nFrancesca is the daughter, son, and grandson of Francesca Gabriello.\nThat’s right, Francesca was a woman, too, and she had a daughter named Gabriella.\nAnd the poem he wrote for her was called Lola di Gabriello.\nThe name Gabriella is the name of a woman from a famous family of Italy, who lived in Rome from 1760-1770.\nSo, what does Gabrielia’s name mean?\nWell, Gabries son’s father, Francescar, is Francesco’s brother and Francesco had a brother named Giovanni who was born when Francesco and Francesca were both children.\nFrancescar is the great-grandson of Giovanni, and Francescar has been a famous writer of fiction and poetry for almost a century.\nFrancesc is known as a poet, and in the 1800s, he wrote his first book, L’Inner Man .\nFrancescias son and his sister, Francesce, have been poets since their youth.\nFrancesces mother is Francesca’s grandmother, and her mother was Francesco’ sister.\nFrancesce was Francesca ‘s grandmother, so she’s a very important figure in the family.\nWhat is the meaning of the name Francesca?\nThe name Francescar means “Mother”.\nIt’s a word that is used in English to refer to a female person.\nIn Italian, the word Francesca is the masculine form of the feminine name Franni."

"What’s in a name? That which we call a rose\nBy any other name would smell as sweet.\nRomeo and Juliet (II, ii, 1-2)\nI love William Shakespeare’s plays and Romeo and Juliet may be his most famous one. Most know the story of the two star-crossed lovers, but I’ll give a brief overview for everyone’s benefit. The Montagues and the Capulets are two rival families that hate each other. Juliet is a Capulet. Romeo is a Montague. They fall in love with each other and it gets everyone killed. It is a wonderful play.\nDuring the play, Juliet remarks about Romeo’s name. She loved him for just being himself. She didn’t care if he was called a Montague. She thought that a rose would remain the same if is had a different name, but Juliet was naïve. If you called roses “poop flowers”, I doubt any woman would want them delivered to their door. It is true that the “poop flowers”, formerly know as roses, would smell good, but who would want to stick their nose in a “poop flower”?\nSo, the name matters. We can just glance at the bible to know this is true. Abram become Abraham because he would be the father of nations. Simon became Peter because it meant “rock”. Saul became Paul. And Jesus’ name would be prophesied by Isaiah. So, names seem to be important according to scripture.\nMatthew 1:23 “The virgin will be with child and will give birth to a son, and they will call him Immanuel”–which means, “God with us.”\nFORGET TO BECOME FRUITFUL\nRecently, I heard a sermon that stuck with me. So, some of the ideas I am about to share are not completely my own, but that doesn’t mean I shouldn’t share them.\nI’ve established an importance in names, especially in the Bible. I think there are direct lessons to be learned from the names given to people in Bible. My example comes from the story of Joseph. I have to admit that I cringe when I read the first half of Joseph’s story. His brothers were jealous of him and they threw him in a ditch. Then they sold him into slavery. Just when things started to look up, he is accused of rape and thrown into prison for many years. There he sat in prison until one day he is given the chance to interpret the Pharaoh’s dreams.\nJoseph interpreted the Pharaoh’s dreams and adverted the Egyptian people from starving. The Pharaoh was so grateful that he made Joseph a ruler of Egypt. To make a long story short, Joseph encountered his brothers during his reign. I’m sure he was full of anger and rage when he saw them, but ultimately he reunites with his family.\nThat is a hard thing for me to swallow. I think I would have tortured them to death, but Joseph eventually embraces them as brothers. How did he do it, though?\nThe answer is in the name’s of his children.\nGenesis 41:51-52 “Joseph named his firstborn Manasseh and said, “It is because God has made me forget all my trouble and all my father’s household.” The second son he named Ephriam and said “It is because God has made me fruitful in the land of my suffering.”\nIt blows my mind how much Joseph had to forget in order to let go. The past seems to always creep up on us, but Joseph’s past must have felt like the worst haunted house film you can imagine. Despite that, he forgot and after he forgot he was fruitful. The past was forgotten and his future was fruitful because of it. Joseph never took credit, either. Both of his son’s names claim that “God Has…”. It was because of God that Joseph could forget and be fruitful.\n“In a word, the Future is, of all things, the thing least like eternity. It is the most completely temporal part of time—for the Past is frozen and no longer flows, and the Present is all lit up with eternal rays….”\nThe Screwtape Letters by C.S. Lewis\nThe Screwtape Letters are written from the perspective of demons that daily attack us. One of the things the devil wants most is for us to be obsessed with the Past or with the Future. The Past is gone and can not be changed, but the devil would love for us to look back and reminisce. He wants us to say, “Gosh, things were so much better back then. I wish things were like that again.”\nOr he wants us focused on the Future. Then the devil wants us to say, “I can’t wait until things get better.” The problem with that is things will never be good enough. Remember, that we are not made for this sinful world. We are designed for holy communion with Christ in heaven. Our time on Earth is brief and we are only here to temper us to be more like Christ.\nUltimately, the devil wants us to see what we don’t have and look back at what we did have, but that is not Christ’s command. He wants us to live in the present. In order to do that we must remember this important verse.\nMatthew 6:34 “Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.”\nSo, we started on names and that lead to forgetting to be fruitful, but ultimately this is about living for today. What are you doing today to further the kingdom of Christ? What does today look like? Tomorrow will be here tomorrow, but today is now. What are you going to do with it? Romeo and Juliet risked it all for love. Abraham changed his name and became a father of a nation. Peter became one of Christ’s closest disciples. Joseph suffered one day at a time in order to become the ruler of Egypt.\nWhat will you do with today?"

"WHAT IS IN A NAME?\nExodus 6:1 – 8\n\"A rose by any other name would smell as sweet\" is a popular reference to William Shakespeare's play Romeo and Juliet, in which Juliet seems to argue that it does not matter that Romeo is from her family's rival house of Montague, that is, that he is named \"Montague\". The reference is often used to imply that the names of things do not affect what they really are. This formulation is, however, a paraphrase of Shakespeare's actual language. Juliet compares Romeo to a rose saying that if he were not named Romeo he would still be handsome and be Juliet's love. This states that if he were not Romeo, then he would not be a Montague and she would be able to get married with no problem at all.\nHowever, God, when he was going to bring about the deliverance of the Nation of Israel from the bondage of Egypt, he wanted to be known by a very special and precise name that would make him distinct from all and any other god. So much so, that he listed it as one of the supreme moral commands for them. “Thou shalt not take the name of the LORD in vain” Ex. 20:7.\nThe translators of the King James Bible had no other option but to put this phrase in it specific format. However, this name is used 6,518 times. It is identified by the term “LORD”. Note that, all the letters are capitalized. It is only transliterated 7 times. four times by itself and three times with special significance. “Jehovah Jireh” – The LORD will provide Gen. 22:14; “Jehovah Nissi” – The LORD has sworn Ex. 17:15; and “Jehovah - Shalom”- The LORD is peace.\nHere in Exodus 6:1 - 8 and 3:14 He give us the meaning and significance of this name and the reason it should be known differently in contrast with all the other names for God.\nIn Exodus 3:14 when Moses is first commanded to go back to Egypt to tell the people that their God has sent him to deliver them, he says to God that they are going to ask him “What is his name?” In reply God says, “I AM THAT I AM” tell them “I AM has sent me.” In the next verse he attaches it to the “God of their Fathers, Abraham, Issac, and Jacob” and explain that it will be his name for them forever.\nWhat this phrase means is that God – IS, and that he is Self-existence and Self determinant and Eternal. The phrase “I AM” is actually verb meaning to be – or become, but because of the phrasing t is given as a noun meaning “I Exist and will always Exist.” Now travel forward to chapters ix where God takes the phrase “I AM THAT I AM” and combines the letter to form the name “JEHOVAH” or “YAHWEH.” But the amazing things that he does is he attaches it to the covenant that he had made to Abraham, Issac, and Jacob. So, the Self – Existing, Self – Determining and Eternal God becomes a covenant keeping God. He attaches to this covenant seven specific promises that he is going to do for them: 1. “I will bring you out” vs. 6. 2. “I will rid you out of their bondage.” 3. “I will redeem you.” 4. “I will take you to me for a people” vs. 7. 5. “I will be to you God.” 6. “I will bring you into the land which I swear” s. 8. 7. “I will give it ou for you for a heritage.”\nThis name of God is to be forever associated with his promises and that he is the same God that rules over the earth. Psalms 83:18 states “That [men] may know that thou, whose name alone [is] JEHOVAH, [art] the highest over all the earth.” The God over all the earth is self – existing, self-determining, eternal and covenant keeping. If he fails in one promise to Israel, then he would not be God. God reminds them constantly that it is for his “Name Sake.” It says in Psalms106:8 “Nevertheless he saved them for his name's sake, that he might make his mighty power to be known.”\nIt would be best for us to know that the God of our Salvation is the Jehovah of Israel, that keep his promises and that places his name on the line if he fails to do what he says. Most importantly, Jesus identified himself as the Jehovah of the Old Testament when he said in the Gospel of John that he was the “I AM.” He says in John 8:58 “Before Abraham was “I AM” and the Jews took up stones to stone him, because he being a man made himself God. His name is attached to our forgiveness of sin (Matt. 1:21; Acts 13:38). His name is attached to our adoption as son (John 1:12) His name is attached to our sustenance for life (John 6:51). His name is attached to our eternal relationship with God (John 17:3). His name is attached to our purpose of suffering (1 Peter 4:16).\nThe name Jehovah and the name Jesus are the names of our God that we should hold in reverence and honor and remember the covenant they have made with us lest we fail to represent them in this evil world.\nWhat is the name of your God? Does the name of your God limit your associations? Have there been an occasion where you have failed to take a stand for the name of your God?"

"While International SBL has already begun, I still have more notes to share on the conference Peter in Earliest Christianity, held by the Centre for the Study of Christian Origins at Edinburgh University.\nThere were several very good papers on the first day of the conference (I already wrote a brief note about a paper given by Larry Hurtado), but the one I found most interesting was given by Prof. Margaret Williams (Edinburgh). Her paper, entitled \"The Nomenclature of Peter - A Brief Enquiry,\" examined the three names of the Apostle: Simon, Peter, and bar Jonah.\nSimon. Noting that Shimon was by far the most common male name among Jews at the time, owing to the popularity of Shimon Maccabee, we can assume that Simon's family was patriotic. Additionally, if we add the others of the Maccabean family (Judas, John and perhaps Joseph), the names associated with the Hasmonean dynasty might make up 40% of all male names. You can imagine then, how many 'Judas son of John son of Judas' or 'John son of Judas son of Simon' there were. The assumption that Simon was the name given to Simon Peter by his parents, according to Williams, is a near certainty.\nBar Jonah. Simon's patronymic name is either 'bar Jonah' (Matt 16:17) or 'bar John' (John 1:42; 21:15). While John is much more common, given the affinity for Hasmonean names, Prof. Williams argues that bar Jonah is more likely. In the Galilee, still quite distinct from the south, the emphasis on Hasmonean names was less and the name Jonah was used a little more often. Add to that the likelihood that the name would change over time from Jonah to John rather than the reverse, and one can assume that the earlier reading is the correct one. It is important to note that with a more unusual name patronymic name, it is likely that there was not another with the name Simon bar Jonah in the fishing village of Bethsaida, and so he may not have required a nickname to distinguish himself.\nPeter. Peter (also Kepha and Cephas), of course, means 'rock.' Williams, with several points of justification, is quite confident that this supernomen was actually assigned to Simon by Jesus (note that this is not the same as believing that Jesus assigned any sort of papal commission to Simon). It was very common for Jews at the time to adopt Aramaic nicknames, given the confusion due to so few Jewish names. These Aramaic names could easily be translated or transliterated into Greco-Roman names in the concern of integration. Life changes often brought about a supernomen; joining a regiment, a household or religious conversion could bring about such a change. One reason that we can be confident that Peter's name was given to him is because the three closest to Jesus have experienced this transition. Along with Peter, James and John were designated boanerges, sons of thunder. Finally, it is important to note that 'rock' is attested to as a nickname in Hebrew, Greek, Aramaic and Latin, so it is not a problem to imagine this as a likely nickname.\nIt was a very interesting overview of the onomastic issues surrounding Peter. While it seems at first to simply confirm much of what we find in the Gospel account (aside from the confusion regarding 'bar Jonah' or 'bar John'), Dr. Williams provided an excellent overview of the context and the issues and practices of names, patronyms and supernomens."

"What’s in a name? that which we call a rose\nBy any other name would smell as sweet.\n— Juliet, Romeo and Juliet, Act II, Scene 2\nIn these well-known words, Juliet expresses her frustration that she and Romeo must be kept apart because he is a Montague, and she, a Capulet. Their family names should make them sworn enemies. But why should names matter? Wouldn’t Romeo still be the same person even if he bore a different name? “George,” perhaps?\nMaybe. But the Bible seems to have a different perspective.\nThe significance of one’s name was once much greater than it is now. God has many names in Scripture, not the least of which is the one considered by Jews as too holy to be uttered (signified in English translations by “LORD” in all caps). And as we’ve seen, even in just the first chapter of John’s gospel, we already have several names for Jesus. That includes his favorite name for himself: Son of Man (John 1:51). All of these names say something about the bearer’s identity and character.\nBut parents today seem less concerned about meanings than how their children’s names will sound. Pity the prophets, who were instructed to give their children names like “Not-loved” (1:6) and “Not-my-people” (1:9) to signal God’s displeasure. Isaiah was even told to name his son “The-spoil-speeds-the-prey-hastens” (Isa 8:1, NRSV), to prophesy the coming of the mighty Assyrian army.\nOne wonders what the other kids called the poor boy when he reached middle school.\nIt’s noteworthy, then, that the very first time Jesus meets Andrew’s brother Simon, Jesus assigns him a new name: “Cephas” (John 1:42), which means “rock.” This is the only place in John (indeed, in all of the gospels) where the name is used, though Paul uses it frequently (e.g., 1 Cor 1:12; Gal 1:18). The rest of the time, John uses the name we’re most familiar with: Peter.\nSimon. Simon bar-Jonah (“son of Jonah/John,” Matt 16:17). Peter. Simon Peter. These names all refer to the same person. He used to be defined by his relationship to his father. But Jesus has given him a new identity: The Rock. Later, Jesus explains the significance of the name: Peter is the steady and sure one upon whom Jesus will build his church (Matt 16:18).\nAnd as soon as Jesus says this, Rocky messes up.\nIt would be too simple to say that Peter gets it all together later, after Pentecost, when he receives the Holy Spirit. Yes, he preaches the gospel mightily and thousands come to Christ at once (Acts 2:14-41). Yes, he is able to perform acts of healing reminiscent of Jesus himself (Acts 3:1-10). And he no longer runs from trouble: he continues to proclaim Jesus even if he has to suffer for doing so (Acts 5:41-42).\nBut he still messes up now and again, as when he gives in to social pressure and breaks fellowship with the Gentile converts in Antioch, earning him a public rebuke from Paul (Gal 2:11-21).\nSo it goes. Not everyone receives a new name upon meeting Jesus. But we do receive new identities. To some extent, those identities are aspirational; they define not only who we are in Jesus, but who we are becoming, who we will be when our sanctification is complete.\nWe will mess up. That’s for certain. But the glorious grace of it all is that while we slouch toward tomorrow, God can and will still use for his kingdom purposes, just as we are today."

"All Algebra 1 Resources\nExample Question #3 : Complex Conjugates\nThe answer must be in standard form.\nMultiply both the numerator and the denominator by the conjugate of the denominator which is which results in\nThe numerator after simplification give us\nThe denominator is equal to\nHence, the final answer in standard form ="

"Complex Analysis refers to the study of complex numbers. In dealing with Complex Analysis, it is important to understand the different terms. A complex number, in Mathematics, is a number that can be expressed in the form a+bi, where ‘a’ and ‘b’ are real numbers, and ‘i’ is the imaginary unit. It is also important to note that i^2=-1. Thus, a+bi is a complex number because it is a mix of real and imaginary, with the ‘a’ being real, and the ‘b’ being imaginary. Complex numbers are often depicted on a plot, where the x-axis represents the real value of the complex number (a) and the y-axis represents the imaginary value of the complex number (b). The point, which is plotted, is thus known as point (a, b). One thing to consider is that numbers written in the a+bi form are not necessarily complex numbers. For example, if a = 0 then the number is purely imaginary. If b = 0, then the number is completely real.\nThe creation of these complex numbers gives an additional tool to solve problems that cannot be solved with just real numbers alone. However, one important realization to note is that these imaginary numbers are no more or less fictitious than any other kind of number. With this in mind, these complex numbers have practical applications in many fields other than Mathematics – most prominently in electrical engineering. For example the imaginary ‘I’ is sometimes used to designate current in power systems. AC circuits in particular have their resistance and reactance denoted by two complex numbers. The sum of these two complex numbers is then known as the impedance, denoted by the symbol Z.\nThus, understanding complex numbers, and by extension Complex Analysis is a crucial skill to possess when dealing with complex problems."

"From Math Images\n|Completing the Square|\n|Simple Harmonic Motion|\nComplex numbers are numbers which take the form , where and are real numbers and .\nSuch numbers frequently appear in mathematical equations, even in those describing physical systems. Extending our notion of numbers to include complex numbers results in many astounding symmetries and relationships throughout mathematics.\nComplex numbers have two parts: a \"real\" part represented by and an \"imaginary\" part represented by ; the factor in the imaginary part forces the two to be separate. The same operations that are used on real numbers, such as addition, subtraction, multiplication, and division, can be used on complex numbers. For example, two complex numbers are added by components, real added to real part and imaginary to imaginary part:\nAs another example, multiplying two complex numbers is carried out in the same way that we would multiply two real binomials:\nNote that because each is the square root of , the product of two terms gives , so .\nVisualizing the Complex Numbers\nWe traditionally visualize the real numbers, such as 2 and 0.5, as points on the number line. We can visualize real numbers this way because all real numbers can be identified by a single value. The real number 5 is unique, and has its own place on the number line. Because complex numbers have two parts, we can think of them as vectors contained in a plane. We call the plane which contains complex numbers the Argand Plane, or the Complex Plane. The y-axis represents the imaginary component of our complex number, and the x-axis the real component. The complex number is shown below:\nWe can thus speak of the magnitude of a complex number as the length of this vector, which is , as is readily shown by the Pythagorean Theorem.\nThis vector idea leads to an important relation between trigonometry and the complex numbers. Euler's formula, which can be derived using Taylor Series, tells us that\n- This page's main image shows that\n- and .\n- Substituting gives\nTherefore all complex numbers of the form can be expressed with an exponential function."

"A Bit About Complex Numbers:\nA complex number has a real and an imaginary component.\nz = x +iy\nThe presence of the i makes these two components linearly independant. Thus we can begin to think of a complex number as a 2D vector. In fact it is convenient to represent a complex number as a (real, imaginary) pair.\nz = (x, y)\nWe know that we can add and subtract complex numbers\nz1 + z2 = (x1 + x2, y1 + y2)\nz1 - z2 = (x1 - x2, y1 - y2)\nz1 - z2 = (x1 - x2, y1 - y2)\nand we acheive the same result as adding and subtracting 2D vectors.\nComplex numbers can do something that 2D vectors can't. You can multiply them.\nz1z2 = (x1x2 - y1y2, x1y2 + y1x2)\nThe existence of the multiplication rule promotes the complex numbers from a mere vector space to an algebra. An algebra is a linear space that has a multiplication rule.\nIf we want the complex numbers to represent a 2D vector space we are missing something, and that's a dot product. In a 2D vector space, we have a dot product that tells us the length of the vectors, (or the length squared of the vectors to be more precise.)\nBut wait!! We can determine the magnitude squared of a complex number as well:\n|z|2 = zz* = (x2 + y2, 0) = x2 + y2\nHere the * represents a complex conjugate, which merely flips the sign of the imaginary component. The magnitude squared of a complex number is identical to the result of taking the dot product of a 2D vector with itself. Using this as your starting point, you can show that the vector dot product, defined in terms of a complex algebra is\nA•B = (1/2) (AB* + BA*)\nWhen endowed with a dot product, the complex numbers truly do contain a full and complete representation of a 2D vector space, with the added bonus of having a well defined way of multiplying the vectors together.\nIn other words, 2D vectors are not complex numbers, but complex numbers ARE 2D vectors which have the added power of multiplication.\nSo What Was Hamilton Thinking?\nOften, when one is looking up information about quaternions, the story comes up about how W.R. Hamilton is walking along one day, and while crossing a bridge he suddenly comes up with the formula for quaternions. He then promptly vandalizes the bridge and goes on his merry way.\nHow does someone just come up with quaternions? I will tell you.\nHamilton was aware of the fact that the algebra of complex numbers supply a natural mechanism for multiplying 2D vectors, and he was wondering: How would a person multiply 3D vectors? We add and subtract 3D vectors, and we have a dot product for 3D vectors, but how do you multiply 3D vectors?\nNow, some people might be thinking, what about the cross product? Why can't the cross product be the multiplication rule for 3D vectors? The answer is: the cross product definitely holds a clue, but it is not the entire answer. Besides, it wasn't until after the invention of the quaternion that we even had a cross product, so Hamilton didn't know about them.\nSo, as Hamilton is crossing the bridge it dawns on him how we might multiply 3D vectors together, and he writes the multiplication rules for the 3D basis vectors on the bridge. These multiplication rules are what we are talking about when we say the \"definition of a quaternion\"\nSo How Did Hamilton Come Up With the Formula?\nRemember how we defined the 2D dot product in terms of the complex multiplication rule? Hamilton similarly decided that if a 3D multiplication rule exists, the result of multiplying a vector with itself should be a real number that is equal to the length squared of the vector. So, however the mutliplication works, it should result in the following formula\nVV† = x2 + y2 + z2\nThe meaning of the † here is similar to that of the complex conjugate, but here it flips the signs of all of the basis vectors.\nV† = -xI - yJ - zK\nThere are nine terms in the product, when the vector is expressed in terms of its 3 components\nVV† = -x2I2 - y2J2 - z2K2 - xy(IJ + JI) - xz(IK + KI) - yz(JK + KJ)\nBy not combining the IJ and the JI terms, I am stating that they are possibly different.\nWhile crossing the bridge Hamilton realized that he could satisfy his initial postulate about the multiplication of 3D vectors, if the basis vectors satisfied the following multiplicaiton rules.\nI2 = J2 = K2 = -1\nIJK = -1\nIJK = -1\nIn other words, if he applied these rules, the first 3 terms would fall out correctly, and the last 6 terms would vanish.\nHamilton was pretty stoked about this, because this meant that you could add, and subtract 3D vectors, but now you could also multiply them together!\nSo Where Does the Fourth Component Come From?\nUsing Hamiltons multiplication rules for the basis vectors, we can define a general multiplication rule for the product of arbitrary 3D vectors.\nAB = -A•B + A×B\nThe first term is a scalar, and the second term is a 3 component vector, four components in all. It was probably this surprising discovery that the multiplication rules summoned the existence of a 4th component that prompted Hamilton to call them quaternions, which literally means \"a group of 4.\"\nThe existence of the 4th component in a general quaternion does not change the original meaning of the vector portion. The vector portion of a quaternion is truly a 3D vector, in every possible identification. It adds, subtracts, and has a dot product like a standard 3D vector. We can use it in every possible way that we can use any 3D vector. The only magic here is that we now have a multiplication law. This is a good thing, since we can use this multiplication law to make meaningful geometric statements about 3D vectors.\nSo What Do Quaternions Have To Do With Rotations?\nAt the very heart of the definition of the quaternion multiplication lies the postulate that it must somehow represent the length of the vector. The fundamental definition of a rotation is that it is a transformation which does not change the length of a vector. Thus the definition of quaternion mutliplication is very intimately connected to the concept of rotation.\nLet's build the rotation from the ground up. To begin with, we know that quaternion multiplication from the right is not the same as quaternion multiplication from the left. Thus, the general form of a transformation would look something like this\nv' = AvB\nWhere we have two transformation quaternions, one acting on the right, and one acting on the left.\nSince v is a 3D vector, we don't care what the scalar part is. However, the transformation should also not care. This means that the transformation should not change the value of the scalar part. If the scalar part starts at zero, the transformation should leave it zero. Placing this restriction on the general form of the transformation leads to the following condition.\nB = A†\nAnd so our transformation law now looks like this\nv' = AvA†\nFinally, we require that the length of v is not changed by the transformation. This can be stated using Hamiltons initial postulate of 3D vector multiplication\nv'v'† = vv†\nAvA† (AvA†) = AvA†Av†A†\nAvA† (AvA†) = AvA†Av†A†\nWe see that the only way our condition can be satisfied is if A†A = 1. In other words A must be normalized. An arbitrary normalized quaternin takes the form\nN = cos(α) + n sin(α)\nHere n is a normalized 3D vector.\nIf we use this N to apply the transformation, we will see that we have successfully rotated v around the axis n by an angle of 2α. The reason for the factor of 2, is because there are 2 factors of N acting on v. To take this into account, we generally define rotation quaternions in terms of a half-angle.\nr = cos(θ/2) + n sin(θ/2)\nYou now know the why behind quaternions. A 3D vector is not a quaternion, but a quaternion IS a 3D vector, with a multiplication law that requires an additional scalar component. Go now, and unleash your newfound power upon the helpless masses."

"Complex numbers are numbers that consist of a real number and an imaginary number. They come in the form of . (With and being real numbers and being the imaginary unit).\nThey add up very much like you would imagine. Take the two complex numbers (2+3i) and (3+4i). Adding the two together is as simple as adding the real parts (in this case: 2 + 3 = 5) and adding the imaginary parts (3i + 4i = 7i) to give us the final complex number of (5 + 7i).\nThe same applies for subtraction. Taking our example complex numbers of (2+3i) and (3+4i). We just subtract the real part (2 - 3 = -1) and subtract the imaginary part (3i - 4i = -i) to give us our new complex number (-1-i).\nMultiplication is much like expanding quadratic and cubic equations. Simply, you just take the two complex numbers, sit them side by side and multiply out. Taking our example complex numbers we would do the following:\nIt really is as simple as thinking of like in our quadratics and treating it in exactly the same way, then replacing with , with and with .\nThe modulus of a complex number is the length of the line that joins the origin of an Argand diagram to the point that represents the complex number, and it is given by:\nThe argument of a complex number is the angle in radians of the complex number point from the real axis (the x-axis), measured counterclockwise. The argument for a complex number z, denoted arg(z), is given by:\nif it is in the first quadrant.\nWhen representing a complex number on an Argand diagram, we can see that\nSince a complex number z can be represented by x+iy,\nA complex number can be represented in either Cartesian or polar form. The polar form is:\nwhere is and is the argument of z.\nThe polar form of a complex number is very similar to how we represent vectors. Accordingly, the modulus of a complex number is analogous to the resultant of the x and y components, and the argument is the direction of the resultant vector.\nEuler's relationship is:\nBy substituting this into the polar form for a complex number, we can see that another way of writing the complex number z is:\nConjugates are just reflections of co-ordinates on an Argand diagram. They are reflected across the real axis and thus only the imaginary co-ordinate is changed (from, say, 2 + 2i to 2 - 2i). In other words, the sign of the imaginary part is changed (from negative to positive or vice versa).\nComplex conjugates are useful when dividing complex numbers as the denominator can be made real by multiplying the top and bottom of the fraction by the complex conjugate of the denominator, for example:\nThis is called realising (the complex number version of rationalising) the denominator.\nConjugates are also useful when solving equations with real coefficients. If such an equation has an complex root, then the conjugate of the complex number will also be a root of the equation, allowing you to factorise the equation fully in most cases in exams.\nIf a polynomial has real coefficients and if any of its roots are complex, then these roots will occur in conjugate pairs.\nExample: Given that is a solution, find the other roots of the equation .\nWe automatically know one of the other roots is (since the coefficients of the polynomial above are all real) so we can start to form a factorization of the equation:\nNow that we know about complex numbers, we can start to solve quadratic equations whose determinant is negative (i.e. quadratics that do not cross or touch the x-axis on a Cartesian graph).\nExample: Solve the equation .\nSince we know that the equation does not have any real roots. Using the quadratic formula:"

"The set of all unit complex numbers forms a group under multiplication. It will be seen that it is ``the same'' group as . This idea needs to be made more precise. Two groups, and , are considered ``the same'' if they are isomorphic, which means that there exists a bijective function such that for all , . This means that we can perform some calculations in , map the result to , perform more calculations, and map back to without any trouble. The sets and are just two alternative ways to express the same group.\nThe unit complex numbers and are isomorphic. To see this clearly, recall that complex numbers can be represented in polar form as ; a unit complex number is simply . A bijective mapping can be made between 2D rotation matrices and unit complex numbers by letting correspond to the rotation matrix (3.31).\nIf complex numbers are used to represent rotations, it is important that they behave algebraically in the same way. If two rotations are combined, the matrices are multiplied. The equivalent operation is multiplication of complex numbers. Suppose that a 2D robot is rotated by , followed by . In polar form, the complex numbers are multiplied to yield , which clearly represents a rotation of . If the unit complex number is represented in Cartesian form, then the rotations corresponding to and are combined to obtain . Note that here we have not used complex numbers to express the solution to a polynomial equation, which is their more popular use; we simply borrowed their nice algebraic properties. At any time, a complex number can be converted into the equivalent rotation matrix\nSteven M LaValle 2012-04-20"

"PLEASE HELP WITH THIS ONE QUESTION\n1) What are the three forms of quadratic functions?\n2) For each of the three forms, when would it be most convenient to have the function in that form?\n3) Create a quadratic function in one of the forms and show how to convert it to another one of the three forms.\nneed more info\ny=3n + 1\nthis is wrong because it says the second number is one less and i added one instead\n(sorry i'm not typing it again just read the other two explanation sections i just typed it'll be the same.)"

"Feel free to modify and personalize this study guide by clicking “Customize.”\nComplete the table.\nThere are multiple forms a number can take. These five bullets all represent the same number:\n- complex number:\n- rectangular point\n- polar point:\n1) Plot the complex number\n- a) What is needed in order to plot this point on the polar plane?\n- b) How could the r-value be determined?\n- c) What is the r for this point?\n- d) How could be determined?\n- e) What is for this point?\n- f) What would look like on the polar plane?\n2) What quadrant does occur in when graphed?\n3) What are the coordinates of z = -3 + 2i in polar form and trigonometric form?\n4) What would be the polar coordinates of the point graphed below?\nChange to polar form\n- For the complex number in standard form find: a) Polar Form b) Trigonometric Form (Hint: Recall that and )"

"How do you calculate polar and rectangular?\nIn general, to convert between polar and rectangular coordinates use the following rules: x = r cos(θ) y = r sin(θ) r = (x2 + y2)1/2.\nWhat is a rectangular equation?\nA rectangular equation, or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane. For example y=4x+3 is a rectangular equation.\nWhat is polar and rectangular form?\nIn Rectangular Form a complex number is represented by a point in space on the complex plane. In Polar Form a complex number is represented by a line whose length is the amplitude and by the phase angle.\nHow do polar coordinates work?\nThe polar coordinates of a point describe its position in terms of a distance from a fixed point (the origin) and an angle measured from a fixed direction which, interestingly, is not “north” (or up on a page) but “east” (to the right). That is in the direction Ox on Cartesian axes.\nHow do you convert to rectangular coordinates?\nTo convert from polar coordinates to rectangular coordinates, use the formulas x=rcosθ and y=rsinθ.\nAre Cartesian and rectangular coordinates the same?\nThe Cartesian coordinates (also called rectangular coordinates) of a point are a pair of numbers (in two-dimensions) or a triplet of numbers (in three-dimensions) that specified signed distances from the coordinate axis.\nWhat are polar coordinates in math?\nIn mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Angles in polar notation are generally expressed in either degrees or radians (2π rad being equal to 360°).\nWhat is polar form?\nThe polar form of a complex number is another way to represent a complex number. The form z=a+bi is called the rectangular coordinate form of a complex number. The horizontal axis is the real axis and the vertical axis is the imaginary axis.\nHow do you do polar coordinates on a calculator?\nEnter the number or expression, then ►Rect . To convert an answer to polar form: Enter the number or expression, then ►Polar . The calculator will display the angle (part of the exponent on e) in radians or degrees according to how you set the mode.\nHow do you divide polar form?\nTo multiply complex numbers in polar form, multiply the magnitudes and add the angles. To divide, divide the magnitudes and subtract one angle from the other."

"When you first began graphing mathematical equations and values, you probably used a Cartesian graph, also known as an x, y or rectangular graph. In this chapter you will be graphing quite a bit on a polar graph, or circular graph. Polar equations and polar graphs can be a bit intimidating, particularly at first. With practice, however, you will likely come to appreciate a number of situations where a polar graph is easier or just makes more sense than a rectangular graph.\nAnother major topic in this chapter is imaginary numbers. You may be thinking, \"If the numbers are imaginary anyway, why should I need to learn about them?\" One reason is that imaginary numbers can become real numbers when multiplied together. It seems strange, but imaginary numbers actually 'convert' to real numbers all the time in mathematics, and every number you have ever seen can be written as a \"complex number,\" which is the combination of a real and an imaginary number!\nAnother interesting section in this chapter is the lesson on using the quadratic formula. You probably remember using the formula in the past, and perhaps even remember the \"discriminant,\" which can be used to identify the number of real solutions to a quadratic equation. Now you will get to learn why all of your prior lessons always specified \"real\" answers, when asking you to find the roots!\nThis chapter focuses on the various uses of cartesian (x, y) graph and polar graph methods.\nThrough the material in this chapter, students should become proficient at:\nConverting values and graphs between polar and cartesian methods.\nIdentifying and graphing imaginary and complex numbers.\nUsing the Quadratic Formula to find the imaginary roots of quadratic equations.\nMultiplying and dividing complex numbers and graphing the solutions on polar and cartesian graphs."

"Is it possible to perform basic operations on complex numbers in polar form?\nYes, of course.\nPolar form is very convenient to multiply complex numbers.\nAssume we have two complex numbers in polar form:\nThen their product is\nPerforming multiplication on the right, replacing\nThe above is a polar representation of a product of two complex numbers represented in polar form.\nRaising to any real power is also very convenient in polar form as this operation is an extension of multiplication:\nAddition of complex numbers is much more convenient in canonical form\nThe first step (getting a sum in canonical form) results is\nConverting this to a polar form can be performed according to general rule of obtaining modulus (absolute value) and argument (phase) of a complex number represented as\nThis general rule states that\n(it's not defined only if both\nAlternatively, we can use these equations to define angle"

"Since is the algebraic expression of in terms of its rectangular coordinates, the corresponding expression in terms of its polar coordinates is\nThere is another, more powerful representation of in terms of its polar coordinates. In order to define it, we must introduce Euler's identity:\nWe'll call the polar form of the complex number , in contrast with the rectangular form . Polar form often simplifies algebraic manipulations of complex numbers, especially when they are multiplied together. Simple rules of exponents can often be used in place of messier trigonometric identities. In the case of two complex numbers being multiplied, we have\nA corollary of Euler's identity is obtained by setting to get\nThis has been called the ``most beautiful formula in mathematics'' due to the extremely simple form in which the fundamental constants , and 0 , together with the elementary operations of addition, multiplication, exponentiation, and equality, all appear exactly once.\nFor another example of manipulating the polar form of a complex number, let's again verify , as we did above in Eq.(2.4), but this time using polar form:\nAs mentioned in §2.7, any complex expression can be conjugated by replacing by wherever it occurs. This implies , as used above. The same result can be obtained by using Euler's identity to expand into and negating the imaginary part to obtain , where we used also the fact that cosine is an even function ( ) while sine is odd ( ).\nWe can now easily add a fourth line to that set of examples:\nThus, for every .\nEuler's identity can be used to derive formulas for sine and cosine in terms of :\nSimilarly, , and we obtain the following classic identities:"

"In this section we will be looking at parametric equations\nand polar coordinates. While the two\nsubjects don’t appear to have that much in common on the surface we will see\nthat several of the topics in polar coordinates can be done in terms of\nparametric equations and so in that sense they make a good match in this\nWe will also be looking at how to do many of the standard\ncalculus topics such as tangents and area in terms of parametric equations and\nHere is a list of topics that we’ll be covering in this\nParametric Equations and Curves An introduction to parametric equations and\nparametric curves (i.e. graphs of\nTangents with Parametric Equations Finding tangent lines to parametric curves.\nwith Parametric Equations Finding the area under a parametric curve.\nArc Length with Parametric Equations Determining the length of a parametric curve.\nSurface Area with Parametric Equations Here we will determine the surface area of a\nsolid obtained by rotating a parametric curve about an axis.\nPolar Coordinates We’ll introduce polar coordinates in this\nsection. We’ll look at converting\nbetween polar coordinates and Cartesian coordinates as well as some basic\ngraphs in polar coordinates.\nTangents with Polar Coordinates Finding tangent lines of polar curves.\nwith Polar Coordinates Finding the area enclosed by a polar curve.\nArc Length with Polar Coordinates Determining the length of a polar curve.\nSurface Area with Polar Coordinates Here we will determine the surface area of a\nsolid obtained by rotating a polar curve about an axis.\nArc Length and Surface Area Revisited In this section we will summarize all the arc\nlength and surface area formulas from the last two chapters."

"7. Polar Coordinates\nFor certain functions, rectangular coordinates (those using x-axis and y-axis) are very inconvenient. In rectangular coordinates, we describe points as being a certain distance along the x-axis and a certain distance along the y-axis.\nA graph using\nBut certain functions are very complicated if we use the rectangular coordinate system. Such functions may be much simpler in the polar coordinate system, which allows us to describe and graph certain functions in a very convenient way.\nVectors also use the same idea. [See more in the Vectors in 2 Dimensions section.]\nOn this page...\nIn polar coordinates, we describe points as being a certain distance (r) from the pole (the origin) and at a certain angle (θ) from the positive horizontal axis (called the polar axis).\nThe coordinates of a point in polar coordinates are written as\nThe graph of the point (r, θ) is as follows:\nThe point described in polar coordinates by `(2, (3π)/4)` would look like this:\nWe use polar graph paper for drawing points in polar coordinates.\nNOTE: Angles can be in degrees or radians for polar coordinates.\nNeed Graph Paper?\n(Polar graph paper included.)\nPlot the points on the following polar grid:\na) (2, 60°) b) (4, 165°) c) (3, 315°)\nConverting Polar and Rectangular Coordinates\nThe conversion from polar to rectangular coordinates is the same idea as converting rectangular form to polar form in complex numbers.\n[See how to convert rectangular and polar forms in the complex numbers chapter.]\nFrom Pythagoras, we have: r2 = x2 + y2 and basic trigonometry gives us:\n`tan\\ theta=y/x` x = r cos θ y = r sin θ\nSo it is the same type of thing that we had with complex numbers.\nWe can use calculator directly to find the equivalent values.\nConvert the rectangular coordinates given by `(2.35, -7.81)` into polar coordinates.\nConvert the polar coordinates given by `(4.27, 168^@)` into rectangular coordinates."

"From the trigonometric identities seem offensive or personal use complex form in complex numbers polar form and the feedback on the opposite sign\nThis bookthe electrical engineering there must be positive real parts and polar form and so we use it only. More error details may be in the browser console. Evaluating Limits at Infinity, desktop, as a constant. Conversion of polar form and try that you can write 𝜋 by eliminating dividing. We will just by adding complex numbers in polar form is to split the magnitude.\nAnd adding their quotient divide a modulus 𝑟 one times 𝑧 written as you for your site it can analyze networks composedof resistors, brighter spots mark moduli near zero.\nThe product in complex numbers polar form in the archimedean spiral\nThis is 𝑧 equals 𝑟 times cos 𝜃 plus 𝑖 sin 𝜃, and also will find the polar form, looks like cookies are disabled on your browser.\nThat we can think about their manipulating two ways to appear flat for having a convenient way that it natural to? We should we multiply these two vectors can be added. What was that cos 𝜃 one yourself, while the boat is. We have the product of the argument, and add the numbers in complex polar form? We do this by eliminating dividing by an imaginary number.\nHow do we can\nThere are two ways that physical problems can be represented using complexnumbers: a simple method of substitution, how to derive the polar form of complex numbers.\nThe previous example of the exponential forms involves finding the same horizontal direction and polar numbers in complex form is the variables a quick look back.\nLearn how to use of polar form by six plus 𝜃 one minus 𝜃, which has three, find the two more about the others. GCT Polar Form of a Complex Number Michael P Hitchman. What is the historical origin of this coincidence? And 𝑤 two signals are represented as shown to complex numbers to rectangular form? All you have to do is write both the real and imaginary part of two numbers.\nWe represent in complex numbers into real parts, since itdeals with and when we cannot find a complex number in polar form of unity are divided containing radical in.\nThis method of complex numbers in science andengineering, with in polar form, andin another form than of adding complex numbers polar form in polar form of one."

"Presentation on theme: \"Complex Numbers in Engineering (Chapter 5 of Rattan/Klingbeil text)\"— Presentation transcript:\n1 Complex Numbers in Engineering (Chapter 5 of Rattan/Klingbeil text) EGR 1101 Unit 5Complex Numbers in Engineering(Chapter 5 of Rattan/Klingbeil text)\n2 Mathematical Review: Complex Numbers The system of complex numbers is based on the so-called imaginary unit, which is equal to the square root of 1.Mathematicians use the symbol i for this number, while electrical engineers use j:orCheck whether your calculator recognizes sqrt of -1.\n3 Two Uses of i and jDon’t confuse this use of i and j with the use of and as unit vectors in the x- and y-directions (from previous week).\n4 A Unique Property of jj is the only number whose reciprocal is equal to its negation:Therefore, for example,\n5 Rectangular versus Polar Form Just as vectors can be expressed in component form or polar form, complex numbers can be expressed in rectangular form or polar form.\n6 Rectangular FormIn rectangular form, a complex number z is written as the sum of a real part a and an imaginary part b:z = a + ib or z = a + jbEx: z = 5 + j2\n7 The Complex PlaneWe often represent complex numbers as points in the complex plane, with the real part plotted along the horizontal axis (or “real axis”) and the imaginary part plotted along the vertical axis (or “imaginary axis”).Plot the previous number (z = 5 + j2)\n8 Polar FormIn polar form, a complex number z is written as a magnitude |z| at an angle :z = |z| The angle is measured from the positive real axis.\n9 Converting from Rectangular Form to Polar Form Given a complex number z with real part a and imaginary part b, its magnitude is given by and its angle is given byConverting between the two forms is exactly the same as for vectors!Do the previous number (z = 5 + j2)\n10 Converting from Polar Form to Rectangular Form Given a complex number z with magnitude |z| and angle , its real part is given by and its imaginary part is given byConverting between the two forms is exactly the same as for vectors!\n11 Exponential Form |z| |z|ej 3/6 3ej/6 Complex numbers may also be written in exponential form. Think of this as a mathematically respectable version of polar form.In exponential form, should be in radians.Polar formExponential Form|z||z|ejOne reason this is important: to enter numbers in polar form in MATLAB, you actually have to enter them in exponential form.Continuing example, write z = 5 + j2 in exponential form.Example:3/63ej/6\n12 Euler’s IdentityThe exponential form is based on Euler’s identity, which says that, for any ,\n13 Mathematical Operations We’ll need to know how to perform the following operations on complex numbers:AdditionSubtractionMultiplicationDivisionComplex Conjugate\n14 AdditionAdding complex numbers is easiest if the numbers are in rectangular form.Suppose z1 = a1+jb1 and z2 = a2+jb2 Then z1 + z2 = (a1+a2) + j(b1+b2)In words: to add two complex numbers in rectangular form, add their real parts to get the real part of the sum, and add their imaginary parts to get the imaginary part of the sum.\n15 SubtractionSubtracting complex numbers is also easiest if the numbers are in rectangular form.Suppose z1 = a1+jb1 and z2 = a2+jb2 Then z1 z2 = (a1a2) + j(b1b2)In words: to subtract two complex numbers in rectangular form, subtract their real parts to get the real part of the result, and subtract their imaginary parts to get the imaginary part of the result.\n16 MultiplicationMultiplying complex numbers is easiest if the numbers are in polar form.Suppose z1 = |z1| 1 and z2 = |z2| 2 Then z1 z2 = (|z1||z2|) (1+ 2)In words: to multiply two complex numbers in polar form, multiply their magnitudes to get the magnitude of the result, and add their angles to get the angle of the result.\n17 DivisionDividing complex numbers is also easiest if the numbers are in polar form.Suppose z1 = |z1| 1 and z2 = |z2| 2 Then z1 ÷ z2 = (|z1|÷|z2|) (1 2)In words: to divide two complex numbers in polar form, divide their magnitudes to get the magnitude of the result, and subtract their angles to get the angle of the result.\n18 Complex ConjugateGiven a complex number in rectangular form, z = a + ib its complex conjugate is simply z* = a ibGiven a complex number in polar form, z = |z| its complex conjugate is simply z* = |z|\n19 Entering Complex Numbers in MATLAB Entering a number in rectangular form: >>z1 = 2+i3Entering a number in polar (actually, exponential) form: >>z3 = 5exp(ipi/6)You must give the angle in radians, not degrees.\n20 Operating on Complex Numbers in MATLAB Use the usual mathematical operators for addition, subtraction, multiplication, division: >>z5 = z1+z2>>z6 = z1*z2 and so on.\n21 Built-In Complex Functions in MATLAB Useful MATLAB functions:real() gives a number’s real partimag() gives a number’s imaginary partabs() gives a number’s magnitudeangle() gives a number’s angleconj() gives a number’s complex conjugate\n22 This Week’s Examples Impedance of an inductor Impedance of a capacitor Total impedance of a series RLC circuitCurrent in a series RL circuitVoltage in a series RL circuit\n23 Review: ResistorsA resistor has a constant resistance (R), measured in ohms (Ω).\n24 Review: InductorsAn inductor has a constant inductance (L), measured in henries (H).It also has a variable inductive reactance (XL), measured in ohms. We’ll see in a minute how to compute XL.\n25 A New Electrical Component: The Capacitor A capacitor has a constant capacitance (C), measured in farads (F).It also has a variable capacitive reactance (XC), measured in ohms.Build the first four columns of a table showing component, abbreviation, unit (& abbrev), and schematic symbol.\n26 Review: Impedance Impedance (Z) Resistance (R) and reactance (X) are special cases of a quantity called impedance (Z), also measured in ohms.Impedance (Z)Resistance (R)Reactance (X)Inductive Reactance (XL)Capacitive Reactance (XC)\n27 Reactance Depends on Frequency A resistor’s resistance is a constant and does not change.But an inductor’s reactance or a capacitor’s reactance depends on the frequency of the current that’s passing through it.Start fifth column (formula for impedance) in table.\n28 Formulas for Reactance For inductance L and frequency f, inductive reactance XL is given by:XL = 2fLFor capacitance C and frequency f, capacitive reactance XC is given by:XC = 1 (2fC)As frequency increases, inductive reactance increases, but capacitive reactance decreases.Start fifth column (formula for impedance) in table.\n29 Frequency & Angular Frequency Two common ways of specifying a frequency:Frequency f, measured in hertz (Hz); also called “cycles per second”.Angular frequency , measured in radians per second (rad/s).They’re related by the following: = 2fComplete fifth column (formula for impedance) in table.\n30 Formulas for Reactance (Again) Using = 2f, we can rewrite the earlier formulas for reactance.For inductance L and frequency f, inductive reactance XL is given by:XL = 2fL = LFor capacitance C and frequency f, capacitive reactance XC is given by:XC = 1 (2fC) = 1 (C)Start fifth column (formula for impedance) in table.\n31 Total ImpedanceTo find total impedance of combined resistances and reactances, treat them as complex numbers (or as vectors).Resistance is positive real (angle = 0) ZR = RInductive reactance is positive imaginary (angle = +90) ZL = j XL = j 2fL = j LCapacitive reactance is negative imaginary (angle = −90) ZC = −j XC = −j (2fC) = −j (C)Add a sixth column (position in complex plane) to table."

"Various concepts are used in mathematics. Radicals are also one among them. They can also be represented with the help of a symbol. Basically they are used to represent the root of a number. The number can from the various number systems in mathematics. There are various number systems in mathematics.\nThe natural number system, whole number system, integer number system and real number system are some of them. There can also be irrational numbers and also complex numbers. The complex numbers have a real part and an imaginary part attached to them.\nDo they are said to be complex numbers. The operations that are performed on real numbers like addition and subtraction can also be performed on the complex numbers as well. But to perform these operations one must be clear with the concept of the complex numbers.\nThe next question that arises is how do you simplify radicals in mathematics. The radicals have to be simplified in order to arrive at the final answer. The process to simplify radicals is quite simple. The root that has been applied to a number can be a square root, cube root and so on.\nSometimes fourth root can also be used. The number inside the square root symbol must be present two times then it can be taken out of the square root symbol. In case of cube root symbol it should be three times and in the case of the fourth root it should four times and so on.\nIn simplifying radicals practice is required; otherwise it becomes very tough to solve the problems. In mathematics practice is very important otherwise it will be very difficult to arrive at the final answer. Many mistakes can also be committed en-route to the answer. This can be avoided by proper practice.\nThere can questions to simplify radicals with variables like the simplification of normal radicals. The process is quite similar to the process of simplification of the radicals of the normal nature. Only proper practice can help one to reach at the right answer. There can be signs that can be used before the radical symbol.\nThe signs can be positive or negative in nature. Depending on the sign preceding the radical symbol the answer also changes. The positive denotes a positive number and a negative sign denotes a negative number. The magnitude also plays a very important role."

"Complex number Representation\n» Abstraction of complex numbers\n→ solution of algebraic equations in 2D plane\n→ eg: x3=1x3=1 has 33 solutions, (3√1)1st(3√)1st, (3√1)2nd(3√)2nd, (3√1)3rd(3√)3rd\n» complex numbers are numerical expressions\n→ eg: 3+44√-5 is one solution to (x-34)4=-5\n» solution to quadratic equation in the form a+ib\nNote: irrational numbers do not have a generic form. But, it is later proven that all complex numbers can be expressed in the form a+ib.\nFor now, only solution to quadratic equation is shown to be in the form a+ib.\nRepresentations of Complex Numbers\n» coordinate form a+ib\n» polar form r(cosθ+isinθ)\nabstracted from a+ib\nWhen using the real numbers, we come across problems that are mathematically modeled as x2=-1. There is no solution to this in real number system. So, the number system is extended beyond real numbers. This number system that is over-and-above the real number system and is named as 'complex numbers'.\nIrrational numbers are represented with numerical expressions or symbols.\nHow a complex number is represented? In this topic an incomplete explanation to the form of representing complex number is discussed.\nIn the topic 'Generic form of Complex Numbers', the information discussed in here is further developed to complete the explanation. Understanding this complete representation with generic form requires some basics to be explained. In due course, the basics are explained and then we'll take up that.\nIn irrational number system, the solution to x2=2 is given as ±√2.\nLearning from that, the solution to x2=-1 is '±√-1'. The solution is represented as a numerical expression (much the same way as irrational number representation).\nNote: In the attempt to develop knowledge in stages, the discussion given in here are specific to quadratic equations. A more generic discussion will follow once first level of knowledge is acquired.\nThe solution to x2=-4 is '±2√-1'.\nThe solution to (x+3)2=-4 is '-3±2√-1'\nIt is noted that a quadratic equation of the form px2+qx+r=0 can be re-arranged to (x+q2p)2=-rp+(q2p)2.\nFor any equation in this form, we can arrive at a solution in the form a+b√-1.\n√-1 is represented with a letter i\nThe solution to a quadratic equation is in the form a+bi.\nNote : The said explanation covers only solutions to quadratic equations. Let us examine this representation in detail and then later generalize this for complex numbers.\nWhat are the solutions to the equation (x-1)2=-16?\nThe answer is '1±4i'.\n[Initial understanding] -- Form of complex number : Solution to quadratic equation is a+bi where a,b∈ℝ and i=√-1\nAll the following equals 2\nA number can be equivalently represented with numerical expressions of various forms.\nGiven hypotenuse is c. All the following represent the length of side opposite to the angle θ in a right angle triangle:\nA constant can be represented as expressions.\nIt was established that solution to quadratic equation is in the form a+bi. An equivalent expression of this is √a2+b2(a√a2+b2+b√a2+b2i)\nA number a+bi is equivalently given as\nThis form looks similar to cos and sin of a right angled triangle.\nIt is equivalently represented as r(cosθ+isinθ) where r=√a2+b2 and θ=tan-1(ba).\nWe know that, sinθ equals sin(θ+2nπ) where n=0,1,2,...\nA number in the form a+bi is equivalently given as\nThe outline of material to learn \"complex numbers\" is as follows.\nNote : Click here for detailed overview of Complex-Numbers\n→ Complex Numbers in Number System\n→ Representation of Complex Number (incomplete)\n→ Euler's Formula\n→ Generic Form of Complex Numbers\n→ Argand Plane & Polar form\n→ Complex Number Arithmetic Applications\n→ Understanding Complex Artithmetics\n→ Addition & Subtraction\n→ Multiplication, Conjugate, & Division\n→ Exponents & Roots\n→ Properties of Addition\n→ Properties of Multiplication\n→ Properties of Conjugate\n→ Algebraic Identities"

"SAT SUBJECT TEST MATH LEVEL 2\nREVIEW OF MAJOR TOPICS\nNumbers and Operations\n3.2 Complex Numbers\nGRAPHING COMPLEX NUMBERS\nA complex number can be represented graphically as rectangular coordinates, with the x -coordinate as the real part and the y -coordinate as the imaginary part. The modulus of a complex number is the square of its distance to the origin. The Pythagorean theorem tells us that this distance is . The conjugate of the imaginary number a + bi is a – bi , so the graphs of conjugates are reflections about the y -axis. Also, the product of an imaginary number and its conjugate is the square of the modulus because (a + bi )(a – bi ) = a 2 – b 2i 2 = a 2 + b2.\n1. If z is the complex number shown in the figure, which of the following points could be iz?\n2. Which of the following is the modulus of 2 + i?"

"If a =2 +i then in the form of a+bi what does a^-1 equal\nFollow Math Help Forum on Facebook and Google+\nOriginally Posted by Rimas If a =2 +i then in the form of a+bi what does a^-1 equal It means the multiplicative inverse,\nOriginally Posted by Rimas What? I multiplied by the \"conjugate\" to clear the denominator from imaginary numbers. Note, I multiplied both the numerator and denominator.\nThe meaning of is definied as the inverse, meaning,\nThis is one of my favorite questions.\nThe multiplicative inverse of a complex number z is:\nView Tag Cloud"

"Calculate the real part, the imaginary part, and the absolute value of the following expression:\ni * [(1+2i)(5-3i)+3i/(1+i)].\nSo I did the math out this way:\ni * [(4+21i)/(1+i)] = (4i-21)/(1+i)\nIs this correct and what do you call the imaginary part and the real part if a denominator exists with an imaginary i?\nThanks for any help.\nSeptember 14th 2006, 01:41 PM\n(1+2i)(5-3i)= 11+7i is correct!\nYou should then rewrite 3i/(1+i)= (3i)(1-i)/2 = (3+3i)/2\ni[(11+7i)+ (3+3i)/2]=(-7+11i)+(-3+3i)/2 =(-17/2)+(25/2)i\nSeptember 14th 2006, 01:59 PM\nI really appreciate the help Plato. I was going to ask how the second part worked but I figured it out. You just multiply it by its conjugate.\nSeptember 14th 2006, 02:07 PM\nThat really is an important point.\nIn general, we do not allow complex numbers written as 1/(a+bi).\nIn fact, the multiplicative inverse is, (a+bi)^(-1) = (a-bi)/(a^2+b^2).\nThat is the conjugate divided by the absolute value squared."

"Complex Numbers: Subtraction, Division\nDate: 08/12/2001 at 23:04:42 From: April Subject: Subtraction and division for imaginary numbers I know that when adding imaginary numbers the formula is (a+bi)+(c+di) = (a+c)+(b+d)i but for subtraction, is the formula (a+c)-(b+d)i ? And how do you divide imaginary numbers - like for instance: a+bi/a-bi?\nDate: 08/12/2001 at 23:39:04 From: Doctor Peterson Subject: Re: Subtraction and division for imaginary numbers Hi, April. The formula for addition works because complex numbers follow the associative and commutative properties just as real numbers do. We can do the same for subtraction, and get (a+bi) - (c+di) = (a+bi) + -(c+di) = (a+bi) + (-c + -di) = a + bi + -c + -di = a + -c + bi + -di = (a-c) + (b-d)i That is, you subtract the real parts and the imaginary parts. For division, we generally think of it as simplifying a fraction, much like the way you rationalize the denominator of a fraction. In this case, you can multiply numerator and denominator by the complex conjugate of the denominator. So in general, we get a+bi (a+bi)(c-di) (ac+bd) + (bc-ad)i ---- = ------------ = ------------------ c+di (c+di)(c-di) c^2 + d^2 Since the denominator is now a real number, you can just divide the real and imaginary parts of the numerator by it to get the answer. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/\nSearch the Dr. Math Library:\nAsk Dr. MathTM\n© 1994-2015 The Math Forum"

"Geometric Intuition of Multiplying Complex Numbers\n- maths partner\nMultiplying Complex Numbers\nSo we have just seen that multiplying by real numbers causes a rotation of either or and multiplying by causes a rotation of so now lets see what happens when we multiply by other complex numbers... If you have a go at the activity below you will find that multiplying by different complex numbers causes a rotation of of lots of angles. Notice as well that the vector is also scaled with each multiplication like before. The question is, how can we determine the amount of rotation and scaling from the complex number? This is what we will explore in more detail in the next few sections..."

"Why Multiply Two Complex Numbers?\nDate: 02/20/99 at 17:14:08 From: Angkit Panda Subject: Multiplication of Complex Numbers in Form of Vectors? Why do we multiply two complex numbers? What does that give us, and how do you graph it? (8 cis 70) * (2 cis 34) = (16 cis 104) How do you get that? What is it used for? Thanks.\nDate: 02/22/99 at 09:00:41 From: Doctor Peterson Subject: Re: Multiplication of Complex Numbers in Form of Vectors? The basic idea behind multipliying complex numbers is a simple application of the distributive property: (a + bi)*(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i Someone discovered that this fits very neatly with the polar (\"cis\") representation of the numbers: (a cis b)*(c cis d) = (a cos(b) + a i sin(b))*(c cos(d) + c i sin(d)) = [ac cos(b) cos(d) - ac sin(b) sin(d)] + [ac sin(b) cos(d) + ac cos(b) sin(d)]i = ac cos(b+d) + ac sin(b+d) = ac cis (b+d) So this method of multiplication of complex numbers comes directly from the angle-sum identities in trigonometry. This gives us a simple way to see complex multiplication in terms of vectors: multiply the lengths and add the angles. But that does not originate in any vector concept; it is simply the natural result of defining multiplication of complex numbers to follow the same rules as real numbers. Addition of vectors is a natural concept; multiplication applies only to complex numbers. Write back if there is something else you need to understand. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/\nSearch the Dr. Math Library:\nAsk Dr. MathTM\n© 1994-2013 The Math Forum"

"What are complex numbers? They’re numbers which are made of a real part, a, and imaginary part, bi, in the form a + bi, note: imaginary and real numbers can never be combined into one term.\nImaginary number allow you to use the root of a negative number, for example √-4 = 2i.\nAdding and subtracting complex numbers is simple; you just treat the real and imaginary parts separately.\ne.g. (2 + 5i) + (7 + 3i) = (2 + 7) + (5 + 3)i = 9 + 8i\ne.g. (6 + 3i) – (4 – 9i) = (6 – 4) + (3 – -9)i = 2 – 6i\nMultiplying complex numbers is the same as multiplying in algebra, but beware: as i = √-1, i2 = -1.\ne.g. (2 + 3i) x (4 + 5i); using FOIL/parrot’s beak method for multiplying brackets you get 8 + 10i + 12i + 14i2 which equals 8 + 22i – 14 so the final answer is – 6 + 22i.\nIn order to divide complex numbers, you must first know their complex conjugate. This is simply switching the sign between the real number and imaginary number from + to – or vice versa. Algebraically this means a + bi turns into a – bi. The pair of complex numbers is called the complex conjugate pair. The convention in mathematics is to call one of them z and the other one z*, it doesn’t matter which is which.\nTo divide two complex numbers, turn them into a fraction, then times both top and bottom by the complex conjugate of the denominator.\ne.g. (10 +5i) divided by (1 + 2i) turns into (10 + 5i)/(1 + 2i) x (1 – 2i)/(1 – 2i) which turns into (10 + 5i)(1 – 2i)/(1 + 2i)(1 – 2i) and by using the method learnt for multiplication above it is easy to solve this fraction to get the answer of 4 – 3i. (Some of you may have met this technique before when rationalising denominators, and will see that the denominator of the combined fraction is the difference of 2 squares)\nSometimes you may be given the roots of a quadratic equation, which are always a conjugate pair. This means the equation will be (x – α)(x –β) or x2 – (α + β)x + αβ.\nComplex numbers can be shown on a type of graph called an Argand diagram. This is the same as your normal type of graph, but now the x-axis is for the real part of your complex number, and the y-axis is for the imaginary part, and the vectors created by the complex numbers all begin from the origin.\nThe modulus of a complex number: │x + iy│= √(x2 + y2)\nThe argument of a complex number (arg z) is the angle θ (usually in radians) between the positive side of the real axis and the vector created by the complex number on an Argand diagram. If z = x + iy, then θ = arctan(y/x). (Note: if when you draw the vector the complex number makes is to the left of the y (imaginary) axis, take you answer for θ away from 180 (if using degrees) or π (if using radians).).\nComplex numbers can also be written in the form z = r(cos θ + isin θ) where r is the modulus, and where θ is between -180 and 180 degrees (or between – π and π).\nAnother property of complex numbers is that if you take any two complex numbers, z1 and z2, then │z1 z2│= │z1││z2│.\nYou can also find the square root of a complex number. To do this you create simultaneous equations.\ne.g. z = 3 + 4i: (a + bi)2 = 3 + 4i then expand to get a2 – b2 + 2abi = 3 + 4i. Then equate the real numbers together in one equation, and the imaginary numbers together in another; a2 – b2 = 3 and 2ab = 4, then solve as you would normal simultaneous equations. In this case the answers are 2 + i and – 2- i.\nThe techniques you’ve learnt so far can also help you solve cubic or even quartic equations.\nCubic equations: either all 3 roots are real, or one is real and the other 2 roots are a conjugate pair, so to solve it divide the cubic by the real answer, then complete the square to find the conjugate pair.\nQuartic equations: either all 4 roots are real, 2 are real and the other 2 are a conjugate pair, or the roots are 2 conjugate pairs.\nThis is all you need to know about complex numbers – I hope you’ve found it useful! And if there are techniques from GCSE and AS/A2 maths I’ve used or mentioned here that you are unsure about, such as diving cubics by (x + a), please comment and I’ll make another post explaining them – I’ve already completed my A-Level maths this year hence why I’ve started with a current I covered from Further Maths a few weeks ago."

"simplify write answer in form a+bi, where a and b are real numbers\nAn answer in the form of a + bi is known as a complex number where a and b are real numbers and i is an imaginary number equivalent to the square root of negative 1 (-1). Although the general form of a complex number is a + bi it can appear as a + bi or a - bi. There are 4 imaginary numbers that you should learn and memorize, these numbers are as follows:\ni = square root of -1\ni^2 = -1\ni^3 = -i\ni^4 = 1\nall powers of i after this are just repeats of the first 4 powers of i.\nAn example of a number in a + bi form would be 3 + 2i which would have been derived from a complex number 3 + √(-4). Hope this is helpful."

"Create a FREE account and start now!\nStudents learn that a complex number is the sum or difference of a real number and an imaginary number and can be written in a + bi form. For example, 1 + 2i and - 5 - i root 7 are complex numbers. Students then learn to add, subtract, multiply, and divide complex numbers that do not contain radicals, such as (5 + 3i) / (6 - 2i). To divide (5 + 3i) / (6 - 2i), the first step is to multiply both the numerator and denominator of the fraction by the conjugate of the denominator, which is (6 + 2i), then FOIL in both the numerator and denominator, and combine like terms."

"Math::Complex - complex numbers and associated mathematical functions\n$z = Math::Complex->make(5, 6); $t = 4 - 3*i + $z; $j = cplxe(1, 2*pi/3);\nThis package lets you create and manipulate complex numbers. By default,\nPerl limits itself to real numbers, but an extra\nIf you wonder what complex numbers are, they were invented to be able to solve the following equation:\nx*x = -1\nand by definition, the solution is noted i (engineers use j instead since i usually denotes an intensity, but the name does not matter). The number i is a pure imaginary number.\nThe arithmetics with pure imaginary numbers works just like you would expect it with real numbers... you just have to remember that\ni*i = -1\nso you have:\n5i + 7i = i * (5 + 7) = 12i 4i - 3i = i * (4 - 3) = i 4i * 2i = -8 6i / 2i = 3 1 / i = -i\nComplex numbers are numbers that have both a real part and an imaginary part, and are usually noted:\na + bi\n(4 + 3i) + (5 - 2i) = (4 + 5) + i(3 - 2) = 9 + i (2 + i) * (4 - i) = 2*4 + 4i -2i -i*i = 8 + 2i + 1 = 9 + 2i\nA graphical representation of complex numbers is possible in a plane (also called the complex plane, but it's really a 2D plane). The number\nz = a + bi\nis the point whose coordinates are (a, b). Actually, it would be the vector originating from (0, 0) to (a, b). It follows that the addition of two complex numbers is a vectorial addition.\nSince there is a bijection between a point in the 2D plane and a complex number (i.e. the mapping is unique and reciprocal), a complex number can also be uniquely identified with polar coordinates:\nrho * exp(i * theta)\nwhere i is the famous imaginary number introduced above. Conversion\nbetween this form and the cartesian form\na = rho * cos(theta) b = rho * sin(theta)\nwhich is also expressed by this formula:\nz = rho * exp(i * theta) = rho * (cos theta + i * sin theta)\nIn other words, it's the projection of the vector onto the x and y\naxes. Mathematicians call rho the norm or modulus and theta\nthe argument of the complex number. The norm of\nThe polar notation (also known as the trigonometric representation) is much more handy for performing multiplications and divisions of complex numbers, whilst the cartesian notation is better suited for additions and subtractions. Real numbers are on the x axis, and therefore theta is zero or pi.\nAll the common operations that can be performed on a real number have been defined to work on complex numbers as well, and are merely extensions of the operations defined on real numbers. This means they keep their natural meaning when there is no imaginary part, provided the number is within their definition set.\nFor instance, the\nsqrt(x) = x >= 0 ? sqrt(x) : sqrt(-x)*i\nIt can also be extended to be an application from C to C, whilst its restriction to R behaves as defined above by using the following definition:\nsqrt(z = [r,t]) = sqrt(r) * exp(i * t/2)\nIndeed, a negative real number can be noted\nsqrt([x,pi]) = sqrt(x) * exp(i*pi/2) = [sqrt(x),pi/2] = sqrt(x)*i\nwhich is exactly what we had defined for negative real numbers above.\nAll the common mathematical functions defined on real numbers that are extended to complex numbers share that same property of working as usual when the imaginary part is zero (otherwise, it would not be called an extension, would it?).\nA new operation possible on a complex number that is\nthe identity for real numbers is called the conjugate, and is noted\nwith an horizontal bar above the number, or\nz = a + bi ~z = a - bi\nSimple... Now look:\nz * ~z = (a + bi) * (a - bi) = a*a + b*b\nWe saw that the norm of\nrho = abs(z) = sqrt(a*a + b*b)\nz * ~z = abs(z) ** 2\nIf z is a pure real number (i.e.\na * a = abs(a) ** 2\nwhich is true (\nGiven the following notations:\nz1 = a + bi = r1 * exp(i * t1) z2 = c + di = r2 * exp(i * t2) z = <any complex or real number>\nthe following (overloaded) operations are supported on complex numbers:\nz1 + z2 = (a + c) + i(b + d) z1 - z2 = (a - c) + i(b - d) z1 * z2 = (r1 * r2) * exp(i * (t1 + t2)) z1 / z2 = (r1 / r2) * exp(i * (t1 - t2)) z1 ** z2 = exp(z2 * log z1) ~z = a - bi abs(z) = r1 = sqrt(a*a + b*b) sqrt(z) = sqrt(r1) * exp(i * t/2) exp(z) = exp(a) * exp(i * b) log(z) = log(r1) + i*t sin(z) = 1/2i (exp(i * z1) - exp(-i * z)) cos(z) = 1/2 (exp(i * z1) + exp(-i * z)) atan2(z1, z2) = atan(z1/z2)\nThe following extra operations are supported on both real and complex numbers:\nRe(z) = a Im(z) = b arg(z) = t abs(z) = r\ncbrt(z) = z ** (1/3) log10(z) = log(z) / log(10) logn(z, n) = log(z) / log(n)\ntan(z) = sin(z) / cos(z)\ncsc(z) = 1 / sin(z) sec(z) = 1 / cos(z) cot(z) = 1 / tan(z)\nasin(z) = -i * log(i*z + sqrt(1-z*z)) acos(z) = -i * log(z + i*sqrt(1-z*z)) atan(z) = i/2 * log((i+z) / (i-z))\nacsc(z) = asin(1 / z) asec(z) = acos(1 / z) acot(z) = atan(1 / z) = -i/2 * log((i+z) / (z-i))\nsinh(z) = 1/2 (exp(z) - exp(-z)) cosh(z) = 1/2 (exp(z) + exp(-z)) tanh(z) = sinh(z) / cosh(z) = (exp(z) - exp(-z)) / (exp(z) + exp(-z))\ncsch(z) = 1 / sinh(z) sech(z) = 1 / cosh(z) coth(z) = 1 / tanh(z)\nasinh(z) = log(z + sqrt(z*z+1)) acosh(z) = log(z + sqrt(z*z-1)) atanh(z) = 1/2 * log((1+z) / (1-z))\nacsch(z) = asinh(1 / z) asech(z) = acosh(1 / z) acoth(z) = atanh(1 / z) = 1/2 * log((1+z) / (z-1))\narg, abs, log, csc, cot, acsc, acot, csch,\ncoth, acosech, acotanh, have aliases rho, theta, ln,\ncosec, cotan, acosec, acotan, cosech, cotanh,\nacosech, acotanh, respectively.\nThe root function is available to compute all the n\nroots of some complex, where n is a strictly positive integer.\nThere are exactly n such roots, returned as a list. Getting the\nnumber mathematicians call\n1 + j + j*j = 0;\nis a simple matter of writing:\n$j = ((root(1, 3));\nThe kth root for\n(root(z, n))[k] = r**(1/n) * exp(i * (t + 2*k*pi)/n)\nThe spaceship comparison operator, <=>, is also defined. In order to ensure its restriction to real numbers is conform to what you would expect, the comparison is run on the real part of the complex number first, and imaginary parts are compared only when the real parts match.\nTo create a complex number, use either:\n$z = Math::Complex->make(3, 4); $z = cplx(3, 4);\nif you know the cartesian form of the number, or\n$z = 3 + 4*i;\nif you like. To create a number using the polar form, use either:\n$z = Math::Complex->emake(5, pi/3); $x = cplxe(5, pi/3);\ninstead. The first argument is the modulus, the second is the angle\n(in radians, the full circle is 2*pi). (Mnemonic:\nIt is possible to write:\n$x = cplxe(-3, pi/4);\nbut that will be silently converted into\nIt is also possible to have a complex number as either argument of\n$z1 = cplx(-2, 1); $z2 = cplx($z1, 4);\nWhen printed, a complex number is usually shown under its cartesian style a+bi, but there are legitimate cases where the polar style [r,t] is more appropriate.\nBy calling the class method\nThis default can be overridden on a per-number basis by calling the\nMath::Complex::display_format('polar'); $j = (root(1, 3)); print \"j = $j\\n\"; # Prints \"j = [1,2pi/3]\" $j->display_format('cartesian'); print \"j = $j\\n\"; # Prints \"j = -0.5+0.866025403784439i\"\nThe polar style attempts to emphasize arguments like k*pi/n (where n is a positive integer and k an integer within [-9,+9]), this is called polar pretty-printing.\nThe old display format style, which can have values\nThere are two new display parameters.\nThe first one is\n# the $j from the above example\n$j->display_format('format' => '%.5f'); print \"j = $j\\n\"; # Prints \"j = -0.50000+0.86603i\" $j->display_format('format' => '%.6f'); print \"j = $j\\n\"; # Prints \"j = -0.5+0.86603i\"\nNotice that this affects also the return values of the\nThe second new display parameter is\nThanks to overloading, the handling of arithmetics with complex numbers is simple and almost transparent.\nHere are some examples:\n$j = cplxe(1, 2*pi/3); # $j ** 3 == 1 print \"j = $j, j**3 = \", $j ** 3, \"\\n\"; print \"1 + j + j**2 = \", 1 + $j + $j**2, \"\\n\";\n$z = -16 + 0*i; # Force it to be a complex print \"sqrt($z) = \", sqrt($z), \"\\n\";\n$k = exp(i * 2*pi/3); print \"$j - $k = \", $j - $k, \"\\n\";\n$z->Re(3); # Re, Im, arg, abs, $j->arg(2); # (the last two aka rho, theta) # can be used also as mutators.\nThe division (/) and the following functions\nlog ln log10 logn tan sec csc cot atan asec acsc acot tanh sech csch coth atanh asech acsch acoth\ncannot be computed for all arguments because that would mean dividing by zero or taking logarithm of zero. These situations cause fatal runtime errors looking like this\ncot(0): Division by zero. (Because in the definition of cot(0), the divisor sin(0) is 0) Died at ...\natanh(-1): Logarithm of zero. Died at...\nNote that because we are operating on approximations of real numbers,\nthese errors can happen when merely `too close' to the singularities\nlisted above. For example\nMath::Complex::make: Cannot take real part of ... Math::Complex::make: Cannot take real part of ... Math::Complex::emake: Cannot take rho of ... Math::Complex::emake: Cannot take theta of ...\nAll routines expect to be given real or complex numbers. Don't attempt to use BigFloat, since Perl has currently no rule to disambiguate a '+' operation (for instance) between two overloaded entities.\nIn Cray UNICOS there is some strange numerical instability that results in root(), cos(), sin(), cosh(), sinh(), losing accuracy fast. Beware. The bug may be in UNICOS math libs, in UNICOS C compiler, in Math::Complex. Whatever it is, it does not manifest itself anywhere else where Perl runs.\nExtensive patches by Daniel S. Lewart <email@example.com>."

"complex number(redirected from C numbers)\nAlso found in: Thesaurus, Encyclopedia.\nAny number of the form a + bi, where a and b are real numbers and i is an imaginary number whose square equals -1.\n(Mathematics) any number of the form a + ib, where a and b are real numbers and i = √–1. See number1\na mathematical expression (a + bi) in which a and b are real numbers and i2=−1.\nA number that can be expressed in terms of i (the square root of -1). Mathematically, such a number can be written a + bi, where a and b are real numbers. An example is 4 + 5i.\nSwitch to new thesaurus\n|Noun||1.||complex number - (mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1|\nmath, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement\nnumber - a concept of quantity involving zero and units; \"every number has a unique position in the sequence\"\ncomplex conjugate - either of two complex numbers whose real parts are identical and whose imaginary parts differ only in sign\npure imaginary number - an imaginary number of the form a+bi where a is 0"

"Week 10: January 18 - 24\nComplex numbers: addition and subtraction\nTwo complex numbers are given. Find their sum or difference.\nEach line contains an example of addition or subtraction of complex numbers. The complex number is given in the format a+bi or a-bi, where a is integer, b is non-negative integer. The real and imaginary part of each complex number is no more than\n109 by absolute value.\nFor each input example, print in a separate line the answer.\n2+3i + 7-4i 12-4i - 5-4i -1-1i - -1-1i 5-2i - -7+12i\n9-1i 7+0i 0+0i 12-14i"

"A complex number is an expression of the form x + iy where x and y are real numbers.\nEither x or y may be equal to zero: real numbers and imaginary numbers are special cases of complex numbers.\nGiven a complex number z = x + iy the real number x is known as the real part of z and the real number y is known as the imaginary part of z.\nThe notation Re is used for real part and Im is used for imaginary part.\nNote that the imaginary part of z is a real number y (NOT iy).\nAdding and Subtracting Complex Numbers\nTo add or subtract complex numbers, we add or subtract their real and imaginary parts separately:\n1) (2 + 3i) + (4 + i) = 6 + 4i\n2) (3 - 5i) - 7i = 3 - 12i\n3) (5 - 4i) + (3 + 2i) - (8 + i) = -3i\n4) 12 - 4i + (3 + 4i) = 15\nMultiplying complex numbers\nTo multiply complex numbers, we use the usual rules and the identity i2 = -1:\n|1) (2 + 3i)(4 + 5i)\n||= (2 × 4) + (3i\n× 4) + (2\n× 5i) + (3i × 5i)\n||= 8 12i + 10i - 15\n||= -7 + 22i\n|2) (2 + 3i)3\n||= (2 + 3i)(2 + 3i)(2 + 3i)\n||= (-5 + 12i)(2 + 3i)\n||= -46 + 9i\nThe complex conjugate\nGiven a complex number z = x + iy, the complex conjugate is given by z*\n= x - iy (pronounced “z starâ€):\nTo find the complex conjugate of any expression, replace i by –i.\n1) (3 + 4i)* = 3 - 4i\n2) (5 - 2i)* = 5 + 2i\n3) (6i)* = -6i\n4) [(2 + 4i)*]* = [2 - 4i]* = 2 + 4i\nThe last expression demonstrates that\nA complex number and its complex conjugate have the property that:\n1) (3 + 4i) + (3 + 4i)* = 3 + 4i + 3 - 4i = 6\n2) (3 + 4i) - (3 + 4i)* = 3 + 4i - 3 + 4i = 8i\n3) 5i + (5i)* = 5i - 5i = 0\n4) 5i - (5i)* = 10i\nComplex conjugate of a product\nThe modulus of a complex number\nA complex number z = x + iy multiplied by its complex conjugate is a real number:\nThe modulus of a complex number z = x + iy is written\n| z | and is equal to the positive square root of the sum of the squares of its real and imaginary parts:\nThe modulus is a real number\nThe quotient of complex numbers\nIn order to simplify an expression with a complex number in the denominator, we multiply both the numerator and denominator by the complex conjugate:\nIn this way, we get a real number in the denominator (the modulus squared of\na + bi)."

"2. A complex number is any number of the form a + bi where a and b are real numbers.\nTo add or subtract two complex numbers, you add or subtract the real parts and the imaginary parts.\n(a + bi) + (c + id) = (a + c) + (b + d)i.\n(a + bi) - (c + id) = (a - c) + (b - d)i.\n(3 - 5i) + (6 + 7i) = (3 + 6) + (-5 + 7)i = 9 + 2i.\n(3 - 5i) - (6 + 7i) = (3 - 6) + (-5 - 7)i = -3 - 12i.\nLet's take specific complex numbers to multiply, say 2 + 3i and 2 - 5i.\n(2 + 3i)(2 - 5i) = 4 - 10i + 6i - 15i2 = 4 - 4i - 15i2\nThe definition of i tells us that i2 = -1 . Therefore,\n(2 + 3i)(2 - 5i) = 4 - 4i -15(-1) = 19 - 4i.\nIf you generalize this example, you'll get the general rule for multiplication\n(x + yi)(u + vi) = (xu - yv) + (xv + yu)i\nWe define the conjugate of a + bi as\nConjugates are important because of the fact that a complex number times its conjugate is real.\nWe define modulus or absolute value of complex number a + bi as . We write modulus of a + bi as |a + bi|.\n|3 + 4i| =\nThe process of division of complex numbers:\nstep 1: Find the conjugate of a denominator.\nstep 2: Multiply the complex fraction, both top and bottom complex number.\nHere is the complete division problem:\nNow, we can write down a general formula for division of complex numbers\nEvery nth - order polynomial possess exactly n complex roots."

"The real part of 3 is 3 and the imaginary part of 3 is 0.\nWork Step by Step\nComplex numbers are written in the form a+bi, with a being the real number and b being the imaginary number. Since there is no \"i\" in this complex number, b must be 0 since i*0 = 0. Therefore a=3, so a is the real part of the number and 0 is the imaginary part."

"The real part of -1/2 is -1/2 and the imaginary part is 0.\nWork Step by Step\nComplex numbers are written in the form a+bi, with a being the real number and b being the imaginary number. Since there is no \"i\" in this number, b must be equal to zero, because i*0 = 0. Therefore, -1/2 must be a, so -1/2 is the real part and 0 is the imaginary part."

"How to Perform Operations with Complex Numbers\nSometimes you come across situations where you need to operate on real and imaginary numbers together, so you want to write both numbers as complex numbers in order to be able to add, subtract, multiply, or divide them.\nConsider the following three types of complex numbers:\nA real number as a complex number: 3 + 0i\nNotice that the imaginary part of the expression is 0.\nAn imaginary number as a complex number: 0 + 2i\nNotice that the real portion of the expression is 0.\nA complex number with both a real and an imaginary part: 1 + 4i\nThis number can't be described as solely real or solely imaginary — hence the term complex.\nYou can manipulate complex numbers arithmetically just like real numbers to carry out operations. You just have to be careful to keep all the i's straight. You can't combine real parts with imaginary parts by using addition or subtraction, because they're not like terms, so you have to keep them separate. Also, when multiplying complex numbers, the product of two imaginary numbers is a real number; the product of a real and an imaginary number is still imaginary; and the product of two real numbers is real. Many people get confused with this topic.\nThe following list presents the possible operations involving complex numbers.\nTo add and subtract complex numbers: Simply combine like terms. For example, (3 – 2i) – (2 – 6i) = 3 – 2i – 2 + 6i = 1 + 4i.\nTo multiply when a complex number is involved, use one of three different methods, based on the situation:\nTo multiply a complex number by a real number: Just distribute the real number to both the real and imaginary part of the complex number. For example, here's how you handle a scalar (a constant) multiplying a complex number in parentheses: 2(3 + 2i) = 6 + 4i.\nTo multiply a complex number by an imaginary number: First, realize that the real part of the complex number becomes imaginary and that the imaginary part becomes real. When you express your final answer, however, you still express the real part first followed by the imaginary part, in the form A + Bi.\nFor example, here's how 2i multiplies into the same parenthetical number: 2i(3 + 2i) = 6i + 4i2. Note: You define i as\nso that i2 = –1! Therefore, you really have 6i + 4(–1), so your answer becomes –4 + 6i.\nTo multiply two complex numbers: Simply follow the FOIL process (First, Outer, Inner, Last). For example, (3 – 2i)(9 + 4i) = 27 + 12i – 18i – 8i2, which is the same as 27 – 6i – 8(–1), or 35 – 6i.\nTo divide complex numbers: Multiply both the numerator and the denominator by the conjugate of the denominator, FOIL the numerator and denominator separately, and then combine like terms. This process is necessary because the imaginary part in the denominator is really a square root (of –1, remember?), and the denominator of the fraction must not contain an imaginary part.\nFor example, say you're asked to divide\nThe complex conjugate of 3 – 4i is 3 + 4i. Follow these steps to finish the problem:\nMultiply the numerator and the denominator by the conjugate.\nFOIL the numerator.\nYou go with (1 + 2i)(3 + 4i) = 3 + 4i + 6i + 8i2, which simplifies to (3 – 8) + (4i + 6i), or –5 + 10i.\nFOIL the denominator.\nYou have (3 – 4i)(3 + 4i), which FOILs to 9 + 12i – 12i – 16i2. Because i2 = –1 and 12i – 12i = 0, you're left with the real number 9 + 16 = 25 in the denominator (which is why you multiply by 3 + 4i in the first place).\nRewrite the numerator and the denominator.\nThis answer still isn't in the right form for a complex number, however.\nSeparate and divide both parts by the constant denominator.\nNotice that the answer is finally in the form A + Bi."

"How to Perform Operations with Complex Numbers\nSometimes you come across situations where you need to operate on real and imaginary numbers together, so you want to write both numbers as complex numbers in order to be able to add, subtract, multiply, or divide them.\nConsider the following three types of complex numbers:\nA real number as a complex number: 3 + 0i\nNotice that the imaginary part of the expression is 0.\nAn imaginary number as a complex number: 0 + 2i\nNotice that the real portion of the expression is 0.\nA complex number with both a real and an imaginary part: 1 + 4i\nThis number can't be described as solely real or solely imaginary — hence the term complex.\nYou can manipulate complex numbers arithmetically just like real numbers to carry out operations. You just have to be careful to keep all the i's straight. You can't combine real parts with imaginary parts by using addition or subtraction, because they're not like terms, so you have to keep them separate. Also, when multiplying complex numbers, the product of two imaginary numbers is a real number; the product of a real and an imaginary number is still imaginary; and the product of two real numbers is real. Many people get confused with this topic.\nThe following list presents the possible operations involving complex numbers.\nTo add and subtract complex numbers: Simply combine like terms. For example, (3 – 2i) – (2 – 6i) = 3 – 2i – 2 + 6i = 1 + 4i.\nTo multiply when a complex number is involved, use one of three different methods, based on the situation:\nTo multiply a complex number by a real number: Just distribute the real number to both the real and imaginary part of the complex number. For example, here's how you handle a scalar (a constant) multiplying a complex number in parentheses: 2(3 + 2i) = 6 + 4i.\nTo multiply a complex number by an imaginary number: First, realize that the real part of the complex number becomes imaginary and that the imaginary part becomes real. When you express your final answer, however, you still express the real part first followed by the imaginary part, in the form A + Bi.\nFor example, here's how 2i multiplies into the same parenthetical number: 2i(3 + 2i) = 6i + 4i2. Note: You define i as\nso that i2 = –1! Therefore, you really have 6i + 4(–1), so your answer becomes –4 + 6i.\nTo multiply two complex numbers: Simply follow the FOIL process (First, Outer, Inner, Last). For example, (3 – 2i)(9 + 4i) = 27 + 12i – 18i – 8i2, which is the same as 27 – 6i – 8(–1), or 35 – 6i.\nTo divide complex numbers: Multiply both the numerator and the denominator by the conjugate of the denominator, FOIL the numerator and denominator separately, and then combine like terms. This process is necessary because the imaginary part in the denominator is really a square root (of –1, remember?), and the denominator of the fraction must not contain an imaginary part.\nFor example, say you're asked to divide\nThe complex conjugate of 3 – 4i is 3 + 4i. Follow these steps to finish the problem:\nMultiply the numerator and the denominator by the conjugate.\nFOIL the numerator.\nYou go with (1 + 2i)(3 + 4i) = 3 + 4i + 6i + 8i2, which simplifies to (3 – 8) + (4i + 6i), or –5 + 10i.\nFOIL the denominator.\nYou have (3 – 4i)(3 + 4i), which FOILs to 9 + 12i – 12i – 16i2. Because i2 = –1 and 12i – 12i = 0, you're left with the real number 9 + 16 = 25 in the denominator (which is why you multiply by 3 + 4i in the first place).\nRewrite the numerator and the denominator.\nThis answer still isn't in the right form for a complex number, however.\nSeparate and divide both parts by the constant denominator.\nNotice that the answer is finally in the form A + Bi."

"How do you find the zeros, real and imaginary, of #y=x^2+3x+7# using the quadratic formula?\nPlug the equation into the formula and solve for x. These will be your zeroes.\nplug in the values from the equation\nthen solve for x...\nThis gives 2 imaginary zeroes, but does not give any real zeroes, and if you graph the equation you will see that the equation does not have any."

"Imaginary numbers allow us to represent the square root of a negative number or the product of a real number and the imaginary unit, j. The square root of a negative number is called a pure imaginary number. The symbol represents the principal square root of a and is never negative.\nIf a is a real number, then is a pure imaginary number and\nThe form a+bj is known as the rectangular form of a complex number, where a is the real part and b is the imaginary part.\nTwo complex numbers are equal if both the real parts are equal and the imaginary parts are equal.\nGiven a+bj and c+dj are two complex numbers. Then, a+bj = c+dj if and only if a=c and b=d.\nExample 2 Solve 4+3j = (x+2) + 7j + yj\nReal parts are equal\nImaginary parts are equal"

"Introduction to Imaginary Numbers - Problem 2 3,769 views\nComplex numbers are a combination of real numbers and imaginary numbers, and are typically written in the form a plus bi. Where a is our real component and bi is our imaginary component. So more specifically if I’m looking at say 5 plus 8i, 8i is an imaginary numbers. So you have the square root of negative 1 we don’t know exactly what that is whereas the 5 part we do just number 5.\nSo whenever we are joining these two numbers, real and imaginary we refer to as a complex number. Important thing to note is that if we deal with a plus bi and b is actually 0, this imaginary piece goes away and just leaves us with a real number which is what we’ve been dealing with all along.\nIf a is 0, we're strictly imaginary no real component, so in essence a plus bi our complex number covers every number we ever talked about, but it also throws in this imaginary part as well. So real component imaginary component formed together, give a complex number."

"Complex numbers consist of two separate parts: a real part and an imaginary part. The basic imaginary unit is equal to the square root of\n-1. This is represented in MATLAB by either of two letters:\nCreating Complex Numbers\nThe following statement shows one way of creating a complex value in MATLAB. The variable\nx is assigned a complex number with a real part of\n2 and an imaginary part of\nAnother way to create a complex number is using the\ncomplex function. This function combines two numeric inputs into a complex output, making the first input real and the second imaginary:\nYou can separate a complex number into its real and imaginary parts using the\nComplex Number Functions\nSee Complex Number Functions for a list of functions most commonly used with MATLAB complex numbers in MATLAB.\n|Floating-Point Numbers||Infinity and NaN|\n© 1994-2005 The MathWorks, Inc."

"Imaginary numbers are numbers that are not real. We know that the quadratic equation is of the form ax2 + bx + c = 0, where the discriminant is b2 – 4ac. Whenever the discriminant is less than 0, finding square root becomes necessary for us. Here, we are going to discuss the definition of imaginary numbers, rules and its basic arithmetic operations with examples.\nImaginary Numbers Definition\nImaginary numbers are the numbers when squared it gives the negative result. In other words, imaginary numbers are defined as the square root of the negative numbers where it does not have a definite value. It is mostly written in the form of real numbers multiplied by the imaginary unit called “i”.\nLet us take an example: 5i\n5 is the real number and i is the imaginary unit.\nWhen this number 5i is squared, we will get the negative result as -25. Because the value of i 2 is -1. This means that the √-1 = i.\nThe notation “i” is the foundation for all imaginary numbers. The solution written by using this imaginary number in the form a+bi is known as a complex number. In other words, a complex number is one which includes both real and imaginary numbers.\nWhat is Complex Number?\nComplex numbers are the combination of both real numbers and imaginary numbers. The complex number is of the standard form: a + bi\na and b are real numbers\ni is an imaginary unit.\nReal Numbers Examples : 3, 8, -2, 0, 10\nImaginary Number Examples: 3i, 7i, -2i, √i\nComplex Numbers Examples: 3 + 4 i, 7 – 13.6 i, 0 + 25 i = 25 i, 2 + i.\nImaginary Number Rules\nConsider an example, a+bi is a complex number. For a +bi, the conjugate pair is a-bi. The complex roots exist in pairs so that when multiplied, it becomes equations with real coefficients.\nConsider the pure quadratic equation: x 2 = a, where ‘a’ is a known value. Its solution may be presented as x = √a. Therefore, the rules for some imaginary numbers are:\n- i = √-1\n- i2 = -1\n- i3 = -i\n- i4 = +1\n- i4n = 1\n- i4n-1= -i\nOperations on Imaginary Numbers\nThe basic arithmetic operations in Mathematics are addition, subtraction, multiplication, and division. Let us discuss these operations on imaginary numbers.\nLet us assume the two complex numbers: a + bi and c + di.\nAddition of Numbers Having Imaginary Numbers\nWhen two numbers, a+bi, and c+di are added, then the real parts are separately added and simplified, and then imaginary parts separately added and simplified. Here, the answer is (a+c) + i(b+d).\nSubtraction of Numbers Having Imaginary Numbers\nWhen c+di is subtracted from a+bi, the answer is done like in addition. It means, grouping all the real terms separately and imaginary terms separately and doing simplification. Here, (a+bi)-(c+di) = (a-c) +i(b-d).\nMultiplication of Numbers Having Imaginary Numbers\n(a+bi)(c+di) = (a+bi)c + (a+bi)di\nDivision of Numbers Having Imaginary Numbers\nConsider the division of one imaginary number by another.\n(a+bi) / ( c+di)\nMultiply both the numerator and denominator by its conjugate pair, and make it real. So, it becomes\n(a+bi) / ( c+di) = (a+bi) (c-di) / ( c+di) (c-di) = [(ac+bd)+ i(bc-ad)] / c2 +d2.\nImaginary Numbers Example\nSolve the imaginary number i7\nThe given imaginary number is i7\nNow, split the imaginary number into terms, and it becomes\ni7 = i2 × i2 × i2 × i\ni7 = -1 × -1 × -1 × i\ni7 = -1 × i\ni7 = – i\nTherefore, i7 is – i.\nKeep visiting BYJU’S – The Learning App and also register with it to watch all the interactive videos.\nPut your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!\nSelect the correct answer and click on the “Finish” button\nCheck your score and answers at the end of the quiz\nVisit BYJU’S for all Maths related queries and study materials\nYour result is as below\n|MATHS Related Links|\n|Slope Of A Line||math integers|\n|three dimensional geometry class 12||Equation Of A Plane|\n|Types Of Control||Cube Root|\n|Complex Numbers||Boolean Algebra|\n|LCM Of Fractions||Volume Of Cuboid|"

"Beginners Complex Analysis\n(1) Use the quadratic formula to solve these equations; express the answers as complex numbers.\nI have more of these but I will try them on my own after I receive help on these.\nThe number x is called the real part of z and is writtern x = Re z. The number y, despite the fact that it is also a real number, is called the imaginary part of z and is writter y = Im z.\n(2) Find Re(1/z) and Im(1/z) if z= x + iy, z . Show that Re(iz)= -Im z and Im(iz) = Re z.\nIf further explanation is needed, please let me know. Thanks for the help!"

"Presentation on theme: \"Objectives Define and use imaginary and complex numbers.\"— Presentation transcript:\n1 Objectives Define and use imaginary and complex numbers. Solve quadratic equations with complex roots.\n2 You can see in the graph of f(x) = x2 + 1 below that f has no real zeros. If you solve the corresponding equation 0 = x2 + 1, you find that x = ,which has no real solutions.However, you can find solutions if you define the square root of negative numbers, which is why imaginary numbers were invented. The imaginary unit i is defined as You can use the imaginary unit to write the square root of any negative number.\n8 Solve and check the equations. x2 = –36x = 09x = 0\n9 A complex number is a number that can be written in the form a + bi, where a and b are real numbers and i = The set of real numbers is a subset of the set of complex numbers C.Every complex number has a real part a and an imaginary part b.\n10 Real numbers are complex numbers where b = 0 Real numbers are complex numbers where b = 0. Imaginary numbers are complex numbers where a = 0 and b ≠ 0. These are sometimes called pure imaginary numbers.Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal.\n11 Find the values of x and y that make the equation 4x + 10i = 2 – (4y)i true . Real parts4x + 10i = 2 – (4y)iImaginary partsEquate the imaginary parts.Equate the real parts.10 = –4y4x = 2Solve for y.Solve for x.\n12 Find the values of x and y that make each equation true. 2x – 6i = –8 + (20y)i–8 + (6y)i = 5x – i\n13 Find the zeros of the function. Think “Complete the Square”f(x) = x2 + 10x + 26x2 + 10x + 26 = 0Set equal to 0.x2 + 10x = –26 +Rewrite.x2 + 10x + 25 = –Add to both sides.(x + 5)2 = –1Factor.Take square roots.Simplify.\n14 Find the zeros of the function. Think “Complete the Square”g(x) = x2 + 4x + 12h(x) = x2 – 8x + 18\n15 Find each complex conjugate. The solutions and are related. These solutions are a complex conjugate pair. Their real parts are equal and their imaginary parts are opposites. The complex conjugate of any complex number a + bi is the complex number a – bi.Find each complex conjugate.B. 6iA i0 + 6i8 + 5iWrite as a + bi.Write as a + bi.0 – 6iFind a – bi.8 – 5iFind a – bi.–6iSimplify.\n16 Check It Out! Example 5Find each complex conjugate.A. 9 – iB.9 + (–i)9 – (–i)9 + iC. –8i0 + (–8)i0 – (–8)i8i\n17 Lesson Quiz1. Express in terms of i.Solve each equation.3. x2 + 8x +20 = 02. 3x = 04. Find the values of x and y that make the equation 3x +8i = 12 – (12y)i true.5. Find the complex conjugate of"

"Complex number does has the same set of basic math operations as normal algebra. The basic operations are the familiar addition, subtraction, multiplication and division.\nThe expression for complex number however differs in that it is splitted into 2 parts, namely, the REAL and IMAGINARY parts.\nFormat: Z = a + ib\nwhere \"a\" represents the REAL part and \"ib\" the IMAGINARY part.\nLet me move on with explanation of the basic math operations below.\nAddition of Complex Number\nZ1 = a + ib, and Z2 = c + id\nIf Z1 + Z2, then (a + ib ) + (c + id).\nHowever, we need to separate the real parts addition from the imaginary parts addition.\nRewriting the above addition of Z1 and Z2, a + c + ib + id ==> (a +c) + i(b + d) answer.\nNOTE: Take care and always be aware that complex number has real & imaginary terms. With that solving complex number is sweet and simple.\nSubtraction of Complex Number\nIf we now perform Z1 - Z2, then the math operation yields (a + ib) - (c + id) .\nThe answer would then be, after taking care of the 2 different terms, a - c + ib - id.\nFinal answer : Z1 - Z2 = (a - c) + i(b - d).\nCommon mistake: Never take care of the sign for id when subtracting after opening brackets. The mistake is a - c + ib + id <== the wrong \"+\" sign of \"id\". The principle of basic algebra (math operations) still applies for Complex Number computation. Multiplication of Complex Number\nIf Z1 x Z2, then (a + ib)(c + id).\nDo not be afraid!\nThe steps are the same as for normal algebra except that we need to take care of the \"i\" terms.\n(a + ib)(c + id) = ac + iad + ibc + i2bd\nSince i2 = -1, the working becomes ac + iad + ibc - bd.\nWe can now see that the last term became a REAL term! Take note of that when performing Complex Number multiplication.\nRewriting ac + iad + ibc - bd into real and imaginary terms,\n==> (ad - bd) + i(ad + bc) answer.\nThe math operations of above examples can be seen to be simple, am I correct?\nIt is really simple! Not a bit complex at all.\nHow about Division of Complex Number?\nLet me break this for a later post. I need to delay explanation of Division operation till I cover a special part in complex number computation which is the \"Conjugate\" concept.\n:) And Hang On ....."

"We know that some of the quadratic equations have no real solutions. That means, the solution of such equations include complex numbers. Here, we have found the solution of a quadratic equation ax2 + bx + c = 0 where D = b2 – 4ac < 0. The chapter discusses, in detail, about the need for complex numbers, , to be motivated by the inability to solve some of the quadratic equations. The chapter also enables the students to learn about the algebraic properties of complex numbers, argand plane and polar representation of complex numbers. Statement of the fundamental theorem of algebra, solutions of quadratic equations (with real coefficients) in the complex number system and the square root of a complex number are also among the topics discussed in the chapter."

"2 Complex/Imaginary Numbers WHAT IS?There is no real number whose square is -25 so we have to use an imaginary numberWHY?“i” is an imaginary number. “i” is equal to the square root of -1BASICALLY: any time you see a negative under a SQUARE ROOT an “i” gets pulled out.\n3 Simplifying Radicals with Imaginary Numbers ALWAYS pull the “i” out first before multiplying together.\n4 Adding & Subtracting Complex Numbers A complex number is a number with “i” in it.Complex numbers can be written in the form :Imaginary partReal partTo add or subtract complex numbers combine the real parts and combine the imaginary parts separately.\n6 Multiplying Complex Numbers You multiply complex numbers like you would binomials. (Double Distribute, Box, FOIL…etc)\n7 Dividing Complex Numbers Remember that we don’t want to leave a radical in the denominator.To simplify a quotient, multiply by the conjugate of the denominator.Conjugate – change only the middle signCONJUGATE =CONJUGATE =CONJUGATE =\n8 Rationalize the Denominator SimplifyImaginary # song\n9 iSince “i” raised to a power follows a pattern you can easily find the answer by dividing the exponent by 4 and using the remainder to simplify.4 goes into 12, 3 times with a remainder of zero.4 goes into 22, 5 times with a remainder of 2What about higher exponents? 4-7?4 goes into 33, 8 times with a remainder of 1"

"Presentation on theme: \"Sullivan Algebra and Trigonometry: Section 1.3 Quadratic Equations in the Complex Number System Objectives Add, Subtract, Multiply, and Divide Complex.\"— Presentation transcript:\nSullivan Algebra and Trigonometry: Section 1.3 Quadratic Equations in the Complex Number System Objectives Add, Subtract, Multiply, and Divide Complex Numbers Solve Quadratic Equations in the Complex Number System\nThe equation x 2 = - 1 has no real number solution. To remedy this situation, we define a new number that solves this equation, called the imaginary unit, which is not a real number. The solution to x 2 = - 1 is the imaginary unit I where i 2 = - 1, or\nComplex numbers are numbers of the form a + bi, where a and b are real numbers. The real number a is called the real part of the number a + bi; the real number b is called the imaginary part of a + bi. Equality of Complex Numbers a + bi = c + di if and only if a = c and b = d In other words, complex numbers are equal if and only if there real and imaginary parts are equal.\nAddition with Complex Numbers (a + bi) + (c + di) = (a + c) + (b + d)i Example: (2 + 4i) + (-1 + 6i) = (2 - 1) + (4 + 6)i = 1 + 10i\nSubtraction with Complex Numbers (a + bi) - (c + di) = (a - c) + (b - d)i Example (3 + i) - (1 - 2i) = (3 - 1) + (1 - (-2))i = 2 + 3i\nExample: Multiply using the distributive property Multiplication with Complex Numbers\nIf z = a + bi is a complex number, then its conjugate, denoted by, is defined as Theorem The product of a complex number and its conjugate is a nonnegative real number. Thus, if z = a + bi, then\nDivision with Complex Numbers To divide by a complex number, multiply the dividend (numerator) and divisor (denominator) by the conjugate of the divisor. Example:\nIn the complex number system, the solutions of the quadratic equation where a, b, and c are real numbers and a 0, are given by the formula Since we now have a way of evaluating the square root of a negative number, there are now no restrictions placed on the quadratic formula.\nFind all solutions to the equation real or complex."

"Most of us are used to the real numbers. Real numbers consist of the whole numbers (0, 1, 2, 3, 4, …), the negative numbers (–1, –2, –3, …), the rational numbers (1/2, 2/3, 3/4, 44/7, …), and the irrational numbers (numbers that cannot be represented by fractions of integers, such as the golden ratio, , or ). All of these can be written in decimal format, even though they may have infinite decimal places. But, when we use this number system, there are some numbers we can’t write. For instance, what is the square root of –1? In math class, you may have been told that you can’t take the square root of a negative number. That’s only half true, as you can’t take the square root of a negative number and write it as a real number. This is because the square root is not part of the set of real numbers.\nThis is where the complex numbers come in. Suppose I define a new number, let’s call it i, where\nWe’ve now “invented” a value for the square root of –1. Now, what are its properties? If I take i3, I get –i, since i3 = i2i. If I take i4, then I get i2i2 = +1. If I multiply this by i again, I get i. So the powers of i are cyclic through i, –1, –i, and 1.\nThis is interesting, but what is the magnitude of , i.e. how far is from zero? Well, the way we take the absolute value in the real number system is by squaring the number and taking the positive square root. This won’t work for i, though, because we just get back i. Let’s redefine the absolute value by taking what’s called the complex conjugate of i and multiplying the two together, then taking the positive square root. The complex conjugate of i is obtained by negating the imaginary part of i. Since i is purely imaginary (there are no real numbers that make up i), the complex conjugate is –i. Multiply them together, and you get that –i*i = –i2 = 1, and the positive square root of 1 is simply 1. Therefore, the number i has a magnitude of 1. It is for this reason that i is known as the imaginary unit!\nNow that we have defined this new unit, i, we can now create a new set of numbers called the complex numbers, which take the form\nwhere a and b are real numbers. We can now take the square root of any real number, e.g. the square root of –4 can be written as\nand we can make complex numbers with real and imaginary parts, like 3 + 4i.\nHow do we plot complex numbers? Well, complex numbers have a real part and an imaginary part, so the best way to do this is to create a graph where the abscissa (x-value) is the real part of the number and the ordinate (y-axis) is the imaginary part. This is known as the complex plane. For instance, 3 + 4i would have its coordinate be (3,4) in this coordinate system.\nWhat is the magnitude of this complex number? Well, it would be the square root of itself multiplied by its complex conjugate, or the square root of\nThe positive square root of 25 is 5, so the magnitude of 3 + 4i is 5.\nWe can think of points on the complex plane being represented by a vector which points from the origin to the point in question. The magnitude of this vector is given by the absolute value of the point, which we can denote as r. The x-value of this vector is given by the magnitude multiplied by the cosine of the angle made by the vector with the positive part of the real axis. This angle we can denote as . The y-value of the vector is going to be the imaginary unit, i, multiplied by the magnitude of the vector times the sine of the angle . So, we get that our complex number, z, can be written as\nThe Swiss mathematician Leonhard Euler discovered a special identity relating to this equation, known now as Euler’s Formula, that reads as follows:\nWhere e is the base of the natural logarithm. So, we can then write our complex number as\nWhat is the significance of this? Well, for one, you can derive one of the most beautiful equations in mathematics, known as Euler’s Identity:\nThis equation contains the most important constants in mathematics: e, Euler’s number, the base of the natural logarithm; i, the imaginary unit which I’ve spent this whole time blabbing about; , the irrational ratio of a circle’s circumference to its radius, which appears all over the place in trigonometry; 1, the real unit and multiplicative identity; and 0, the additive identity.\nSo, what bearing does this have in real life? A lot. Imaginary and complex numbers are used in solving many differential equations that model real physical situations, such as waves propagating through a medium, wave functions in quantum mechanics, electromagnetic phenomena, and fractals, which in and of themselves have a wide range of real life application."

"Real numbers and imaginary numbers are each examples of complex\nFor example, we can combine the real number 5 and the imaginary\nnumber 4i to form the complex number, 5 + 4i.\nA complex number is a number that can be written in the form a + bi, where a and b are real numbers and\n• The real number a is called the real part of the complex number.\n• The real number b is called the imaginary part of the complex\nHere are some examples of complex numbers:\n- In the complex number a + bi, the\nimaginary part is b, not bi.\n- In a complex number a + bi, a and b can\nbe any real numbers, including zero.\na + bi\n-8 + 12i\n15 - 7i\n6 + 0i\n0 - 2i\nA complex number whose imaginary part, b, is 0, is called a real number.\nFor example, the complex number 6 + 0i can be written as 6.\nThe number 6 is a real number.\nThis means that the real numbers are a subset of the complex numbers.\nAll real numbers are complex numbers of the form a + 0i.\nAll real numbers are complex numbers.\nHowever, not all complex numbers are\nA complex number whose imaginary part, b, is not 0, is called an imaginary number.\nFor example, the complex number 6 + 4i is an imaginary number.\nThe imaginary numbers are a subset of the complex numbers.\nA complex number whose real part, a, is 0, is called a pure imaginary\nFor example, the complex number 0 - 2i can be written as -2i. The number -2i is a pure imaginary number.\nNext we will study the arithmetic of complex numbers. That is, we will\nlearn how to add, subtract, multiply, and divide them.\nBefore we do so, it will be helpful to define what it means for one\ncomplex number to be equal to another complex number.\nDefinition — Equality of Complex Numbers\nTwo complex numbers are equal if their real parts are equal and\ntheir imaginary parts are equal.\nThat is, a + bi = c + di if a = c and b = d.\nHere, a, b, c, and d are real numbers.\nHere are some examples:\n3 + 5i = (7 - 4) + 5i since 3 = 7 - 4\n8 + 2i = 8 + (1 + 1)i since 2 = 1 + 1\n8 + 7i = 7i + 8 since the real part of each complex\nnumber is 8 and the imaginary part of\neach is 7."

"Presentation on theme: \"Chapter 4: Polynomial and Rational Functions 4.5: Complex Numbers\"— Presentation transcript:\n1Chapter 4: Polynomial and Rational Functions 4.5: Complex Numbers Essential Question: What are the two complex numbers that have a square of -1?\n24.5: Complex Numbers Properties of the Complex Number System The complex number system contains all real numbersAddition, subtraction, multiplication, and division of complex numbers obey the same rules of arithmetic that hold in the real number system with one exception:The exponent laws hold for integer exponents, but not necessarily for fractional onesWe don’t need to worry about this for now, I just needed to list the exceptionThe complex number system contains a number, denoted i, such that i2 = -1Every complex number can be written in the standard form:a + bia + bi = c + di if and only if a = c and b = dNumbers of the form bi, where b is a real number, are called imaginary numbers. Sums of real and imaginary numbers, numbers of the form a + bi, are called complex numbers\n34.5: Complex Numbers Example #1: Equaling Two Complex Numbers Find x and y if 2x – 3i = yiThe real number parts are going to be equal2x = -6x = -3The imaginary number parts are going to be equal-3i = 4yi-3/4 = y\n64.5: Complex Numbers Powers of i Example #4: Powers of i i1 = i i3 = i2 • i = -1 • i = -ii4 = i2 • i2 = -1 • -1 = 1i5 = i4 • i = 1 • i = iAnd we keep repeating from there…Example #4: Powers of iFind i54The remainder when 54 / 4 is 2, so i54 = i2 = -1\n74.5: Complex Numbers Complex Conjugates The conjugate of the complex number a + bi is the number a – bi, and the conjugate of a – bi is a + biConjugates multiplied together yield a2 + b2(a – bi)(a + bi) = a2 + abi – abi – b2i2 = a2 – b2(-1) = a2 + b2The conjugate is used to eliminate the i from the complex number, and is used to remove the use of i in the denominator of fractions\n84.5: Complex Numbers Example #5: Quotients of Two Complex Numbers Simplifymultiply top & bottom by the conjugate of the denominator\n94.5: Complex Numbers Assignment Page 300 Problems 1-35 & 55-57, odd problemsShow work where necessary (e.g. FOILing, converting to i)Due tomorrow\n10Chapter 4: Polynomial and Rational Functions 4 Chapter 4: Polynomial and Rational Functions 4.5: Complex Numbers (Part 2)Essential Question: What are the two complex numbers that have a square of -1?\n114.5: Complex Numbers Square Roots of Negative Numbers Because i2 = -1, In general,Take the i out of the square root, then simplify from thereExample #6: Square Roots of Negative Numbers\n124.5: Complex Numbers Complex Solutions to a Quadratic Equation Find all solutions to 2x2 + x + 3 = 0\n134.5: Complex Numbers Zeros of Unity Find all solutions of x3 = 1 Rewrite equation as x3 - 1 = 0Use graphing calculator to find the real roots (1)Factor that out(x – 1)(x2 + x + 1) = 0x = 1 or x2 + x + 1 = 0\n144.5: Complex Numbers Assignment Page 300 Problems (odd) (skip 55/57, you did that last night)Due tomorrowYou must show work"

"This preview shows page 1. Sign up to view the full content.\nUnformatted text preview: lied a number by its conjugate. There is a nice\ngeneral formula for this that will be convenient when it comes to discussion division of complex\nnumbers. ( a + bi ) ( a - bi ) = a 2 - abi + abi - b2i 2 = a 2 + b 2 So, when we multiply a complex number by its conjugate we get a real number given by, ( a + bi )( a - bi ) = a 2 + b 2\nNow, we gave this formula with the comment that it will be convenient when it came to dividing\ncomplex numbers so let’s look at a couple of examples. Example 3 Write each of the following in standard form.\n2 + 7i\n1 + 2i\n6 - 9i\nSo, in each case we are really looking at the division of two complex numbers. The main idea\nhere however is that we want to write them in standard form. Standard form does not allow for\nany i's to be in the denominator. So, we need to get the i's out of the denominator.\nThis is actually fairly simple if we recall that a complex number times its conjugate is a real\nnumber. So, if we multiply the n...\nView Full Document\nThis note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.\n- Spring '12"

"\"We must have a pie. Stress cannot exist in the presence of a pie.\" - David Mamet\nWhile most of us can thoroughly agree with Mamet, his sentiment does not always extend to the crust. For some reason, people fear pie crust.\nPerhaps that's because of how many strict rules appear in the recipes. The ingredients must be cold. You must not overwork the dough. You must not put too much water in the mix. But really, rules aside, pie crust is a fairly simple thing to make. True, to hone it to an art may take time and require some trial and error, but really, doesn't just about anything worthwhile?\nThat is to say that it's well worth the time to try this simple (and forgiving) classic pie crust recipe.\nBut first, a brief primer on the basics and the \"rules\", so that you can confidently start rolling down a rewarding road of pastry.\nUnderstanding the ingredients\nThere are four ingredients in a typical pie crust: flour, fat, liquid,and salt. But what do these ingredients all do, exactly?\n- Flour (usually all-purpose) gives the crust its bulk and structure.\n- Fat (usually butter, lard, shortening, or a combination) gives the aforementioned structure a flaky texture and gives it flavor.\n- Liquid (usually water) binds the dough and keeps it workable.\n- Salt not only enhances the flavor of both the crust and the filling, but it also helps the crust brown to a pleasing golden hue.\nNote: Different crusts may call for different ingredients, but this is a fairly common roster.\n1. Chill the water and fat.\nCardinal pie crust rule: Always chill the fat (butter, margarine, shortening or lard) and liquid before you begin. Why? This keeps the fat from getting creamed into the flour, which can give the dough an awkward texture.\n2. Don't overwork the dough.\nYou want to handle the dough as little as possible, particularly once you start adding the water. You'll add it gradually, mixing it gently after each addition, only adding enough so that the dough will clump together into a ball in your hand. If the dough is overworked, it can make the pie crust chewy and tough, which isn't always a kind complement to a delicate filling.\n3. Split the dough and roll it into disks.\nMany pie crust recipes will actually make two crusts, and therefore splitting the dough is easily explained: this is so that you'll have a top and bottom crust separated, making for easy logistics when you're rolling it out. If your recipe only calls for a bottom crust, then lucky you -- you've got a pie crust all ready for next time. Why flatten the dough balls into disks? This makes it easier to roll flat once you're ready to bake.\n4. Chill the dough.\nThe dough needs to rest in the refrigerator for at least 30 minutes, or as long as overnight. There are a few reasons: This time allows the flour to absorb all of the liquid; it lets the dough \"relax\" and become more pliable and elastic (and therefore easier for you to handle); and it keeps the fat sealed in specific spots rather than spreading, which will give the crust a nice, flaky and light texture when baked.\n5. Flour your work surface.\nRolling the dough is quite easy. But it's a huge bummer to roll out a perfect round of dough and realize it's stuck to your work surface because it wasn't properly floured. Be generous with the sprinkling of flour on your work surface. This will also help when you are pressing it into the pan and fluting the edges -- it won't stick to your hands as much.\n6. Most importantly: Remain calm.\nAlthough pie crust recipes may be rule-laden, even if you mess up something (adding too much water, overworking the dough, or accidentally adding salted instead of unsalted butter), you'll learn from the experience. And most likely, the pie will still get eaten. So chill. And enjoy. Pie need not be a stressful food!\nPie Crust Recipe\nYield: Either two 9-inch crusts or pastry for one double crust\n- 2 cups all-purpose flour, plus more for rolling the pastry\n- 1 teaspoon salt\n- 1 cup unsalted butter, cut into pieces and chilled\n- 1/3 cup ice water (you may not use all of it)\nNote: Although this recipe calls for butter, feel free to substitute lard or shortening or a mixture for the recipe.\nIn a large bowl, combine flour and salt.\nCut the chilled butter into the dry mixture using a pastry cutter or by using two forks as if they were ninja knives to \"cut\" the fat into the flour. You want the largest crumbs to be no larger than the size of a pea. (There will be smaller crumbs, too -- that is OK).\nIf you have one, you can also use a food processor: pulse the flour with half the butter until it has the texture of a coarse meal. Add the remaining butter and pulse until it's the size of small peas.\nOnce the butter is combined with the flour and salt, turn the mixture into a large bowl.\nStir in the water, one tablespoon at a time, stirring gently with a fork after each addition. Once the mixture clumps together into a ball with minimal dough flaking off, you've added enough water.\nDivide the dough in half, and shape into balls. Flatten each into a disk. Wrap in plastic, and refrigerate for at least 30 minutes, or as long as overnight.\nNote: You will want to refer to your pie recipe before proceeding with rolling out the dough. Some recipes (such as lemon meringue pie) will call for a pre-baked (or \"blind baked\") crust, in which case, you will roll out a single crust and bake it before adding fillings. Other recipes (many fruit pies, for instance) will call for you to roll out a bottom crust, let it chill before adding the filling, then top with the second crust and bake. Keep in mind that the following instructions will be more appropriate for the latter type of recipe.\nFlour your work surface and your rolling pin generously. You'll flour your hands, too, but unwrap the dough first.\nTo roll out your bottom crust, place your dough on the floured surface. Using a rolling pin (or, if you don't have a rolling pin, a heavy bottle such as a wine bottle or glass water bottle with smooth sides will work), begin to roll the pie dough. It will become easier to roll as you work it. Lift a corner to check that it is not sticking to the work surface.\nRoll the dough so that it's about 4 inches wider in circumference than your pie plate. You can check this out by placing your pie plate facedown on top. Try to get the crust as round as possible, but it need not be perfect.\nThen, remove the pie plate and turn it right side up, and have it at the ready.\nFold the pie crust in half, then in half again, so it is in fourths. This will make it easier to transfer to the plate, where you can unfold it.\nYou know those raggedy edges? It's time to either trim them, or if you would like a fluted crust or just like a really thick crust, fold them under the crust so they are hidden, but so that they bolster the edge of the crust on the pie plate, maximizing your crust pleasure.\nIf you'd like to flute the crust, simply pinch it in regular intervals to form a fluted shape.\nIf you've trimmed off excess pieces of crust, don't throw them away! Make them into \"pie fries\" by rolling them up with butter and cinnamon sugar, and baking them in the residual heat of the oven after you bake your pie. You won't regret it!\nIf you're making a double-crusted pie, you'll keep the top crust in the refrigerator until it's called for in the recipe.\nYou can roll out the top crust in the same way you did the bottom one, but it only needs to be about 2 inches larger than the pie plate because you don't have to account for the distance of the sides of the plate.\nTransfer to the top of the pie, and be sure to cut some holes to help vent the steam that will be created once the filling gets hot in the oven.\nOf course, a straightforward top crust isn't the only thing you can do with that second crust. You can top the pie with cutouts using a cookie cutter, or even create a lattice crust. Here are some inspiring decorative pie crust ideas.\nBake according to your pie recipe. Be very proud of yourself: you've made a pie crust!\nJust breaking the crust\nThis is just the beginning! If you want to really perfect your pie-making skills check out the brand new Craftsy class The Art of the Pie Crust with Evan Kleiman. Evan will walk you through making a wide range of pie crusts and their specifications (including what kinds of fats and binders to use), and provide several delicious pie recipes.\nPhoto via Evan Kleinman\nTomorrow on the Craftsy Blog, we'll show you how to make delicious doughnuts at home."

"Adventures of a Culinary Padawan\nÉcole des Techniques à la Cuisine\nLesson Eight: Tartes\nDear Foodie Voyeur,\nThere is nothing wrong with an American apple pie. It's a culinary delight, long-cooked so the apples grow tender. We normally put flour or cornstarch in with the apples as a thickener so it doesn't go all runny. The crust is flakey and tender, and it magically holds the pie together, so it's edible, too, not like the original Henry VIII era pies that are the English predecessor to our pies.\nFrench apple pie is a completely different beast. It's thin, whereas with our pies, the thicker the better! The apples are cooked as a compote for a french tarte, and the top decorated with fans of thinly sliced apples. The crust is not so much a way to hold the pie together, as it is a tender, frangible complement to the filling.\nPie or tarte crust is a bugbear for many. First, the difference -- a tarte is an open, one-crust filled concoction, either savory or sweet, and normally quite thin, no more than an inch thick. A pie is generally deeper and as mentioned, has a more sturdy crust, and often a top crust as well. In the US, we tend to use this only for sweet-filling concoctions, but in England, etc., meat and vegetable pies are also available, but they tend to use flakey pastry these days. Pot pies are actually descended from a soupy vegetable and meat filling topped with noodle dough; the modern version uses flakey pastry also, and only on top.\nThe key to a tender crust is to not touch it very much, and to keep everything cold. The idea is not to activate the gluten protein in the flour -- it activates as soon as liquid or fat is introduced to it. What does it do? The proteins \"crosslink\" -- meaning they stretch and form webs of protein strands, resulting in the stretchy dough texture that's good for bread (thus, hard or \"bread\" flour is a high-protein flour), but not good for pies and cakes (low protein soft or \"cake\" flour). Using all-purpose flour (a mixture of hard and soft flours) is fine, but you need to let the dough \"rest\" in the refrigerator to let the proteins relax and not crosslink. The colder the dough and the less you handle it, the more tender and frangible the crust.\nThis is where a dough scraper is useful. You can mix and chop with it without your hands touching the mixture, meaning it stays cooler and less \"crosslinky.\" Also, you'll be making it on the counter, so make sure it's clean (wipe with vinegar, then buff dry) and cool. If you've bought a marble slab, this is when you should use it.\nFor pâte brisée, pile the flour onto the counter, and sprinkle in the salt (add sugar for a sweet pâte sucrée). Using the scraper, \"chop\" in and mix the dry ingredients (alternatively, you can put them all in a sieve and sift). Have the butter very very very cold, and chopped into cubes -- keep them cold while you're preparing everything else. If you must keep them on the counter, put them in a bowl over an ice bath. Pile the dry ingredient flat, then scatter the small cubes of butter over, then use your scraper to cut and chop the butter and coat the pieces with flour till the mixture takes on a yellowish color from the butter and the pieces are about the size of a split pea. Again, spread the mixture out. Beat together an egg with 2 teaspoons of water (cold, of course!) and sprinkle just over half of it over the flour/butter mixture. Use the scraper again to mix. If you need some more liquid, add a bit more, but the final texture is very crumbly, but will hold together if you softly squeeze a fistful together. It shouldn't be too damp -- the more liquid, the tougher the crust. (Cover and place the leftover eggwash in the refrigerator -- you'll need it later if you are blind-baking.)\nLightly press the pile together to form a crumbly ball. This next step is called fraisage, which is using the heel of your hand to \"smear\" the dough. That is the extent of the mixing. Really! It works. Take a golfball-sized bit of dough, press it together, then smear it out across your counter surface. Scrape up the ribbon of dough and put aside. Repeat till you've made lots of smears. Pile them all together and pat out into a disc. Cover with two layers of plastic wrap, and place in the refrigerator for a MINIMUM of 30 minutes. You might want to write the time and type of crust with a marker on the plastic wrap (savory or sweet). You can freeze these for a month, if you wish.\nPrepare a tarte pan -- this is a flat round metal tray with a ring that sits on top of this. Grease these with beurre pomade -- softened butter -- use your hands or a bit of toweling. On a cold surface, roll out the dough, working from the center outwards. Rotate the dough disk and roll again. Do not roll back and forth. Don't worry if it cracks, we can patch it up later. For a long-cooking tarte, roll to about ¼ inch thick. For a quiche or shorter-baking time tarte, roll about half as thin. It should be significantly larger than the tarte round.\nRoll up the dough around the rolling pin, then roll out over the tarte ring. Life up the edges and tuck into the sides and corners. You can either cut off any excess with scissors or a knife, or run the rolling pin over the edge of the tarte pan. Remove the scraps and put aside. Take a nut-size bit of dough and make what the British call a \"podger\" (no, it's not an official term!). Ball it up, and tamp it against the edge to tuck the dough into the corners of the tarte.\nIt's not advisible to decorate the edges. The ring that forms the shallow edge of the tarte needs to be lifted off the base, and if you excessively decorate and overlap the edge, you'll need to break that edge to de-pan the tarte. Just tidy up the edge or simply crimp it. If you get breaks or holes in your dough, patch them by using some leftover pastry and eggwash to stick the dough onto itself.\nFor quiche, use the pâte brisée and lightly dock the dough. This means take a fork and poke the dough all over without penetrating to the bottom. Lay foil within, and fill with pie weights or dried beans that you use just for baking \"blind\" (nothing in it ... like a blind person has no eyes ... I guess?). Place the whole thing in the refrigerator for 15 minutes, so that the butter in the dough doesn't melt immediately when placed in the oven. Bake in a 325°F / 145°C oven for about 15 minutes, then lift out the foil (save the beans in their own jar for another crust). The au blanc crust should appear a bit chalky -- it's par-cooked, not cooked all the way through, so it shouldn't be browned. Using the reserved egg-water mixture, brush the bottom and sides of the crust to \"seal\" the pastry -- this way, the custard is less likely to run out or soak through. Pop back in the oven for about 3 minutes to set the egg, then remove, leave to cool, and fill as you wish.\nBaking blind is done when the filling cooks in a very short time -- about 15 minutes. If you are cooking something for longer, it's not necessary to par-bake the tarte pastry. A quiche, which is an egg-based custard, cooks quickly, so the crust -- as well as the filling components -- needs to be pre- or par-cooked so they get a head-start. Otherwise, they will remain raw when the custard is done, or the custard will go all hard and grainy waiting for the crust to finish.\nQuiche Lorraine à l'Oignon\nThe Jedi Master told us to combine the Quiche Lorraine (bacon, cream, eggs, cheese) and the Tarte à l'Oignon (sweated lardons, onions, and eggs, cream) recipes. The lardons are sweated in a bit of butter, then the emmincer-cut onions are added with a bit of water, then cooked slowly à l'étové under parchment. These are piled into the par-cooked crust, the sprinkled over with grated gruyère cheese. In a pitcher or batter bowl, beat together equal parts cream and milk, a couple of eggs, salt, cayenne pepper and parsley hacher, then pour over all to about half the depth of the tarte (you may not need it all). Place in the oven for about 20 minutes and serve hot or at room temperature.\nTarte des Pommes\nThe apple tarte needs to cook for about an hour; the pear frangipane tarte, about 30 minutes. Both are simply prepared in the tarte pan, then the dough refrigerated while the innards are cooked or prepped. The longer cooking apple tarte shell should be rolled out a bit thicker than for the frangipane tarte.\nFor the apple tarte, peel and core 4 apples, and cut each apple into 8 wedges, then crosswise into 4, for a total of 32 chunks per apple. Add lemon juice, a bit of sugar to taste and water, then cook à l'étové under parchment until they are softened but still hold their shape. You can use any apple EXCEPT red delicious. This is the compote. Cool over an ice bath, then pile into the chilled, uncooked crust, flattening out and leveling.\nPeel, halve, and core three more apples. Rub with a cut lemon to prevent browning, then slice these thinly, about 1/16th inch or 1/32nd inch in width. Keep the slices together so that the apple half holds it's shape. Place over the top of the compote, then fan out the slices so it forms a ring or spiral along the edges of the tarte. Cover the compote completely with these slices. The slices can also be trimmed down to form a rosette in the center. Pat melted butter over the apple slices, then bake for an hour till the edges of the apples are browned and the crust cooked. Cool to room temperature, and if desired, heat up some apricot preserves with water and strain, then glaze the tarte for a shiny finish.\nTarte aux Poires à la Frangipane\nMake a frangipane by making a pastry cream (crème patissière), then creaming butter and sugar, then blanchir with eggs and almond flour (crème d'amondes). Mix three parts pastry cream to one part almond mixture (this is the frangipane), and spread onto the bottom of the prepared, chilled, uncooked tarte shell, about a quarter to half the way up. This will expand significantly when baked, so don't put more than that. Slice canned, drained pear halves perpendicular to the direction of the stem, and fan four half slices symmetrically over the frangipane. Bake till the frangipane is puffy and browned, and the pastry crust is cooked.\nAll of these can be served hot or at room temperature, not cold or chilled. The Quiche and Frangipane, being egg-based, should be refrigerated if they are going to be stored. A good rule of thumb! Well, maybe rule of tummy?\nSee, tarte shells are easy! Just don't touch them!\nSusu, the Culinary Padawan\n* * * * *\nIntroduction | Glossary | Lessons: One | Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Eleven | Twelve | Thirteen | Fourteen | Fifteen | Sixteen | Seventeen | Eighteen | Nineteen | Twenty | TwentyOne | TwentyTwo\nDisclaimer: All contents are personal observations, and no profit or lucre is expected, solicited, advocated or paid by anyone, including those being observed. This is all just for fun. Any comments, please e-mail the author or WOOKIEEhut directly. Flames will be ignored. This report may not be posted anywhere without the author's knowledge, consent, and permission."

"At its most basic, pie crust is nothing more than flour, fat, and liquid. But if that's all it is, why is pie crust so notoriously difficult to make by hand? Let's take a look:\nFlour: Flour is there for strength, structure, and elasticity. It's the binder that holds the other ingredients together and, well, makes the pastry a pastry! For pie crusts, we usually use regular all-purpose flour instead of cake or pastry flour because we want some gluten development for structure, but not too much.\nRemember - mechanical action creates gluten, so it's important not to over-handle the dough.\nFat: You can use butter, vegetable shortening, lard, or even oil in pie crust, each to a different effect. Butter provides the most flavor and a wonderful melting quality in the mouth, but it tends to not make the most tender pastry. Shortening and lard make a very tender pastry, but don't always have the best flavor for a sweet pie.\nAlso, if the fat is left in large pieces, the crust will be more flaky. If it's incorporated into the flower more thoroughly, the crust will be tender and crumbly.\nLiquid: The liquid in a pie crust creates the steam that lifts the pastry and creates flakes. It also gets absorbed into the flour, helping to create gluten. Too little liquid and the dough won't hold together, but add too much and you'll end up with a rock-hard crust!\nSalt: It might sound odd to have salt in a sweet pie crust, but a pinch or two actually helps boost the flavor without making the crust taste salty.\nSugar: Not all pie crusts have sugar, but those that do will be more tender since sugar interferes with gluten development. In our experience, sugar can also make the pie dough so tender that it's hard to roll out and transfer to your pan without breaking.\nEgg: This makes the dough more pliable and easy to roll out. Eggs also make the crust more compact.\nAcid and Alcohol: Both acid and alcohol tenderize pie dough, make it easier to roll out, and prevent it from shrinking in your pan. If these things give you trouble, try substituting a teaspoon of the liquid with lemon juice or a tablespoon or two with liquor. Vodka is often used because it won't affect the flavor of the dough.\nDo you have a favorite recipe for pie dough?\nRelated: Recipe: Basic Pie Crust"

"Definitions for tortetɔrt; Ger. ˈtɔr tə; ˈtɔr tn\nThis page provides all possible meanings and translations of the word torte\nRandom House Webster's College Dictionary\ntortetɔrt; Ger. ˈtɔr tə; ˈtɔr tn(n.)(pl.)tortes\na rich cake made with eggs, ground nuts, and usu. no flour.\nOrigin of torte:\n1955–60; < G < It torta < LL tōrta (panis) round loaf (of bread)\nrich cake usually covered with cream and fruit or nuts; originated in Austria\nA rich, dense cake, typically made with many eggs and relatively little flour (as opposed to a sponge cake or gu00E2teau).\nOrigin: From Torte\nA torte is a rich, usually multilayered, cake that is filled with whipped cream, buttercreams, mousses, jams, or fruits. Ordinarily, the cooled torte is glazed and garnished. A torte may be made with little to no flour, but instead with ground nuts or breadcrumbs, as well as sugar, eggs, and flavorings.\nFind a translation for the torte definition in other languages:\nSelect another language:"

"A torte and a tart may sound similar and it’s easy to assume that they’re just two names for the same thing, perhaps referring to sweet treats that most of us look forward to after a meal.\nBut tortes and tarts are actually different things, and it would help to know just what their differences are for the next time you visit your favorite bakery.\nTorte vs Tart – What is the Difference?\nTorte vs Tart. A torte is a rich, layered sweet cake made mostly of eggs, ground nuts, or breadcrumbs and contains very little to no flour. It is denser and richer compared to regular cake, but it is also filled with an assortment of fillings and frostings. A tart looks very similar to a pie except that it is not covered and while usually sweet, it can be savory as well. Tart crusts are thicker and crumblier compared to pies, and their fillings are more delicate, usually unbaked or lightly baked.\nTorte vs Tart – What is the Difference?\nWhile their names may sound similar, tortes and tarts could not be more different. In terms of form, tortes are more similar to cakes (it is a type of cake after all), while tarts more closely resemble and in fact can even be confused with pies.\nTortes, like most cakes, are multi-layered (Read: How Many Boxes of Cake Mix For A Three Layer Cake?) and are frosted with various fillings like fruit, cream, chocolate, and nuts, and if you didn’t know any better, you would just assume it is just like any other normal cake.\nTarts have thick crusts with shallow borders, that are filled with either sweet or savory fillings but are not covered with an additional sheet of dough on top as what would normally happen for pies (although some pies can be uncovered, too).\nFor the common person without knowledge of the technical differences in pastry dough used for a tart and a pie, a tart would just look like a regular pie, albeit with shallower edges.\nTortes are said to have originated in Central Europe; from Austria, Germany, or Hungary, while Tarts have their origins in France.\nAll About Tortes – A Closer Look\nWhat is a Torte?\nA torte is a type of cake that is said to have come from Central Europe. Unlike regular cake, flour does not feature a prominent role in making tortes. Most tortes use only a small amount of flour, if at all.\nInstead of flour, eggs, ground nuts, and bread crumbs are used to create multiple layers that are then assembled and filled with various types of rich fillings to create a look that would almost be indistinguishable from a regular cake, until you’ve had a taste.\nTortes vs Cakes\nSo, what’s the difference between tortes and cakes? We’ll explore key differences below.\n1. Ingredients Used\nThe basic ingredients of cake are usually flour, sugar, salt, fat, eggs, and liquid. Depending on the ratio of ingredients and type of flour used, they produce cakes in varying degrees of lightness. Tortes use very little flour, if any, and rely instead on ground nuts or breadcrumbs to replace the flour.\n2. Height of Layers\nTortes, because of the nature of the ingredients used, tend to have shorter layers and denser and heavier textures compared to a regular cake.\nThey do not rise as much, that is why it’s common for tortes to have 3-4 layers but still look shorter or look just about the same height as a regular 2-layer cake. The ingredients used are heavier and therefore do not leaven as much.\n3. Types of Fillings Used\nTortes also tend to be richer, because of the kind of fillings that are usually used. Fruit or jam fillings, ground nuts, whipped cream, mousses, or chocolate ganache are more commonly used, which can be heavier and richer compared to the lighter buttercreams and custard-type fillings of a typical cake.\nTorte layers would also be sometimes brushed with or soaked in liquor-infused syrups for added moisture, which can result in them being denser and more filling.\nSo, there you have it, three basic things that can help distinguish tortes from the typical cake that we are used to seeing. Of course, those differences are not always clear-cut and can get blurred quite easily, especially in cases of fresh and new innovations in flavor combinations.\nBut traditionally speaking, the ingredients, fillings, and the feature of its layers would always distinguish tortes from the rest of their cake family.\nThe Most Famous Tortes\nThere are many different types of tortes and many different types of flavor combinations, but there are a few popular and iconic ones that have become an integral part of the cultures they have originated from. We’ll explore some of those here.\nSachertorte of Vienna\nArguably the most famous chocolate cake in the world, the Sachertorte was invented in Austria in 1832 by a 16-year-old apprentice chef named Franz Sacher.\nThe Austrian State Chancellor Prince Klemens Wenzel von Metternich wanted a dessert that will impress the pants out of his dinner guests, but it just so happened that the head chef got sick that day, and the extraordinary task was left to the young apprentice chef.\nApparently, he was one to rise to the challenge and was someone that can perform under extreme pressure (or perhaps he was already prepared for this for a long time and seized the opportunity to showcase his skills!), and unveiled the very first, the original Sachertorte that evening.\nMuch to the delight of the guests, and the chancellor, an iconic cake was born.\nThe Sachertorte is a dense, multilayered cake filled with apricot jam in between layers, and covered with a chocolate glaze icing. It is a staple cake in most Viennese coffee shops.\nI’ve had the privilege of trying the most famous one at Hotel Sacher in Vienna a few years ago, and I must say, it truly is divine.\nSchwarzwalder Kirschtorte of Germany\nAlso known as Black Forest Cake, this is one of the most well-known German desserts. Layers of chocolate cake are filled with whipped cream and cherries and sometimes topped with shaved chocolate.\nTraditionally, a specialty liquor known as Schwarzwalder Kirsch, distilled from sour cherries, is added to the cake, giving it its distinct flavor.\nDobos Torte from Hungary\nVery thin layers of buttery sponge cake, sometimes soaked in liquor, are filled with chocolate buttercream, topped with shiny, hardened caramel and sometimes covered in ground hazelnuts, chestnuts, or almonds. It is loved for its simplicity and elegance.\nSo there you have it, just a few of the more famous tortes that have captured the hearts (and tummies) of many around the world.\nAll About Tarts – A Closer Look\nWhat is a Tart?\nA tart is a shallow pastry filled with either sweet or savory fillings that can be baked or unbaked. It is similar in appearance to pie, but unlike pie, it only has a bottom crust.\nTarts are said to have originated in France, and the crust is typically made with traditional French shortcrust pastry dough. When made into small, miniature versions, they are called “tartlets”.\nTarts vs. Pies\nIf you see a tart in a pastry shop, especially when it is sitting next to a pie, you are not likely to even give it a second thought and would just probably think it was a type of pie.\nIt would be understandable, though, as they look pretty similar to each other.\nThe fact is, there are actually a number of differences between them. We’ll explore those below.\n1. Form and Shape\nUnlike pies that would usually have both a top covering and bottom crust, tarts only have a bottom crust (although there are some types of pie that do not have this top covering).\nTart crusts are thicker and crumblier while pie crust is usually thinner and flakier. Tarts are also shallower than pies and typically have straight sides.\nWhile pies are usually served in the pan they are baked in, tarts are usually unmolded and served without the support of a pan.\n2. Type of Dough Used for Crust\nTart crust is typically made from traditional shortcrust pastry doughs, which consists of flour, butter, water, and sometimes sugar.\nShortcrust doughs are called such because they require twice as much flour as they do fat. The resulting texture is more biscuit-like and will crumble more easily.\nPies, especially American-style pies like pumpkin pie (Read: “How To Tell if Pumpkin Pie is Done“), are made with dough that consists of similar ingredients: flour, butter, water, and salt, but the way that they are mixed and the proportions of the ingredients result in a flakier, airier crust.\n3. Type of Filling\nBoth tarts and pies do well with sweet and savory fillings, but as tart shells are more delicate and shallower and may crumble more easily, and because they are unmolded and not served in a pan, they do well with fillings that are lighter like creams and custards.\nFillings that are too heavy may cause the shells to break apart, which isn’t too much of a problem with pies.\nTarts and pies are incredibly similar and one would be forgiven to mistake one for the other. But it would be good to know their specific technical differences to ensure that you choose the right method and ingredients the next time you make either one of them.\nTarts are popular the world over and you are likely to find a local version of a tart anywhere you go. We’ll mention some of the most famous ones below.\nTarte Normande or French Apple Tart is a classic tart that comes from the region of Normandy, known for its apples and apple brandy (known as Calvados).\nThe crust is made of pate brisee, a traditional French shortcrust pastry, and is usually served warm with crème Fraiche on the side.\nPastel de Nata\nPastel de Nata is a traditional Portuguese egg custard tart with a flaky crust and a rich but not too sweet filling that is sprinkled with cinnamon and powdered sugar.\nThe original and most famous one is called Pastel de Belem, originally created by monks at the Jeronimos Monastery in Santa Maria de Belem in Lisbon.\nI’ve also had the privilege of tasting these famous egg tarts in Lisbon, and I crave them to this day.\nPopular in the UK, Bakewell tarts consist of a shortcrust pastry shell layered with jam, frangipane, or almond-flavored custard and topped with flaked or sliced almonds.\nThose are just some examples of well-known tarts, but really, there is a treasure trove of them that are worth looking into in your culinary exploration of the world of pastry.\nFrequently Asked Questions to Torte vs Tart – What’s the Difference?\nWhat is a Torte?\nA torte is a type of thin-layered cake that is mostly made with eggs, ground nuts, or breadcrumbs and typically very little to no flour. It is usually denser and richer than other types of cake and is usually filled with jam, fruit, whipped cream, or chocolate ganache, and sometimes soaked in liquor.\nWhat is the Difference Between a Pie and a Tart?\nTarts and pies both consist of a crust filled with either a sweet or savory filling, but tarts do not have the top covering of most pies and are left open and uncovered. Tart shells are thicker and crumblier in texture while pies are thinner and flakier. Tarts are unmolded from the pan after baking while pies are usually served in the pan they are baked in.\nConclusion to Torte vs Tart- What’s the Difference?\nTortes and tarts may sound like they are similar but are actually very different types of food. Tortes are a type of cake, which means that the flavor profiles are only of the sweet variety.\nTarts, on the other hand, are more similar in form to pies in that they always involve some type of shortbread crust, and their flavor profile can either be sweet or savory."

"Difference Between Pie and Tart\nPie vs Tart\nAmong all the known pastries in the world, two of which are easily confused with each other: the pie and the tart. They may look the same as both have fillings and crusts, but they actually differ in a lot of aspects.\nIn terms of shape, pies are round pastries having sloped edges. The dimensions are usually 9 inches wide and 1.5-2 inches thick. The edge of the pie can be designed as purely flat or slightly fluted. The pans used to make this pastry are ordinarily made of Pyrex glass, ceramic, and even pure metal. Initially, it is in the mind of the pastry chef to ensure that the pie crust is big enough for it to cover the entire pan from its base towards its lipped edges. After the filling has all been placed inside, the crust is then cut in a circular fashion about its lip and then pressed towards the edge.\nTarts differ aesthetically because they can take almost any shape. Most are round or oblong-shaped while others tend to be square. The tart can be as short as 4 inches or as long as 1 foot (depending on its shape of course). With regard to the baking pans used to make tarts, it is somewhat shallower as opposed to traditional pie pans. It is just about 0.75 inches to 2 inches deep. Most pastry chefs use metal pans with straight sides and removable bottoms to bake tarts.\nWith regard to their crusts, the pie crust is arranged a little differently. Pies have its crust covering the sides, bottom, and even a fully covered top although open tops are nowadays very common. On the contrary, the tart’s crust rarely covers the top of the pastry. In terms of texture, pie crusts are flaky, light, and crisp while the tart crust is firm and crumbly sometimes even thicker than pie crusts.\nLastly, pies and tarts differ in terms of serving presentation. Because of the ingenious design of the tart pan having a removable bottom, the tart can be cleanly set on the serving plate. Pie pans are usually served using the same pie pans used in baking them.\n1.Pies are usually round while tarts have more freedom of shapes (oblongs, oval, squares, and even some irregularly formed).\n2.Pies are baked using ceramic, Pyrex, or metal pans while tarts often use metal pans.\n3.Pie crusts can cover the top of the pie while tart crusts rarely cover the top of the pastry.\n4.Pie crusts are flakier, lighter, and crisper while tart crusts are firmer and crumblier.\n5.Pies are usually immediately served using the actual pie pans used in baking them whereas tarts are first cleanly removed from the pan and then placed on serving plates.\nSearch DifferenceBetween.net :\nEmail This Post : If you like this article or our site. Please spread the word. Share it with your friends/family.\nLeave a Response"

"What Is The Difference Between Pies And Tarts\n- November 30, 2021\nWhile pies and tarts are two distinct things, they are close enough cousins that we will accept them both. .\nTart vs. Pie: Differences and Delicious Recipes\nShare on Pinterest Nedrofly/Getty Images What is it about pie that makes feel all warm and gooey inside?While both pie and tarts are (usually) desserts with two main components, a baked crust, and a filling, there are a few marked differences between the two and some careful things to consider when making either, like choosing ingredients and deciding when and where to serve them.A standard tart crust contains flour, sugar, salt, and a beaten egg, all incorporated together in a food processor and then chilled before use. .\nWhat is the Difference Between Pies and Tarts? (with pictures)\nCrust thickness, preparation methods and the final appearance also distinguish between pies and tarts.Once the filling is added, the pie crust is cut in a circle around the lip and pressed into the fluted edge.Tart pans are almost always made from metal and have straight sides, sharp edges and a removable bottom.Alternatively, tarts can be baked on a cookie sheet with a pastry ring as support, which also allows for clean removal. .\nPie Tart Difference\nYet the terms aren’t interchangeable, even if the products are equally delicious for dessert (or a savory pie for dinner).Both tarts and pies comprise a pastry crust with a filling that can be sweet or savory.Both tarts and pies comprise a pastry crust with a filling that can be sweet or savory.While both pie and tart crusts use the same ingredients (flour, shortening, cold water, salt and sometimes sugar), they are in different proportions for different purposes.While both pie and tart crusts use the same ingredients (flour, shortening, cold water, salt and sometimes sugar), they are in different proportions for different purposes.Pie crusts are thin, soft, flaky pastry that can be made with different types of shortening.Tart crusts are traditionally made with butter to achieve a buttery pastry flavor.Tarts have firm fillings, based on more eggs or other binders.This is especially important since the tart is free-standing—no pie plate for juices to run onto. .\nDifference Between Pie and Tart\nPie and tart are two baked dishes that consist of a crust and a filling.A pie can have a bottom crust, top crust or both.Many pies have crusts that cover the filling.But tarts have only one crust; their filling is not covered.Therefore, the main difference between pie and tart is that tarts have open fillings whereas pies (some) can have covered fillings.What is a Pie.A filled pie or bottom crust pie has pastry at the bottom of the dish, and the filling is placed on the pastry.What is a Tart.The tart filling can be either sweet or savory.Pies can have a bottom crust, top crust or both crusts. .\nTart vs Pie/Pie vs Tart: Similarities and Differences\nThis post is part of my Fundamental Friday series in which I answer your baking and pastry questions.For ease of browsing, you can find all of the Fundamental Friday posts in one place.Definition of tart: a dish baked in a pastry shell : PIE: such as.a: a small pie or pastry shell without a top containing jelly, custard, or fruit.Pie: a baked dish of fruit or meat and/or vegetables with pastry on the bottom, sides and top.Tart: an open pie filled with sweet food such as fruit.I consulted with my good friend and cookbook author, Jamie Schler, to get the French definitions.In French, the word pie refers either animal coloring (as in piebald) or a bird (as in magpie).A tarte can be sweet or savory, has no sides–so just built on a disc of pastry–or short sides, and no top crust.On pie v tart lecture day, I craned eagerly forward, waiting for the answer to this pastry mystery.Tart pans look different than pie pans.” This is where I began some serious internal muttering.The good news is: I neither lunged over the table at her nor cursed exceptionally loudly.Since there are no hard and fast rules, other than height, my therapist helped me to I see the difference between the two as more of a qualitative one.No doubt pies and tarts are related, but often the similarities and differences are just a matter of degree.Peanut butter and chocolate and marshmallow cream and toffee pieces?American big-ass fruit and cream pies are the Hummers of the pastry world.Tarts are European sports cars: the perfect marriage of form and function delivered in a relatively small, precision package.Tart dough is rich, sandy and flavorful, and the fillings are generally made to complement or contrast with the crust nicely.The other option for a French tart dough is a round of puff pastry.This version of American pie dough uses a combination of shortening and butter to make a crust that contains less water (shortening is 100% fat while butter is about 80-82% fat plus water and milk solids).You can just as easily use puff pastry and rely on all that glorious butter to add flavor.If you need an answer more urgently, please email me, and I will respond within about 4 hours (unless I’m sleeping) and often much more quickly than that.If you make this recipe and/or have enjoyed or learned from reading this post, I’d appreciate it if you could share this!Also feel free to tag me on Instagram at @onlinepastrychef with #pcorecipe so I can find your creation.Thanks for spending some time with me today as we mull the differences between pies and tarts. .\nDifference Between Pie and Tart\nThe pans used to make this pastry are ordinarily made of Pyrex glass, ceramic, and even pure metal.Initially, it is in the mind of the pastry chef to ensure that the pie crust is big enough for it to cover the entire pan from its base towards its lipped edges.After the filling has all been placed inside, the crust is then cut in a circular fashion about its lip and then pressed towards the edge.Most pastry chefs use metal pans with straight sides and removable bottoms to bake tarts.1.Pies are usually round while tarts have more freedom of shapes (oblongs, oval, squares, and even some irregularly formed). .\nDifference Between Pie and Tart\nTarts and pies are baked dishes that are usually sweet and very yummy to eat because of their filling.There are a lot of similarities in the world of pies and tarts to confuse people though they savor the taste of these baked delights.This article attempts to highlight the differences between tarts and pies to enable readers to use the terms correctly.Finally, a round shape cover with the same dough is made and pressed over the filling, to complete the pie before placing it inside the oven. ."

"When distinguishing between pies and tarts, the two sweet treats have a startling resemblance. They’re produced in the same way in a circular dish, have the same appearance, and even taste the same. This article will assist you if you find it difficult to distinguish between the two. Continue reading to learn more about pies and tarts and the differences between them.\n|Pies have a thin crust.||They have a thicker crust|\n|The goal is a crisp, flaky crust.||The goal is a firm, crumbly crust.|\nA pie is a baked item with a crust and a filling that can be sweet or savory. A pie dish’s or pan’s sides are slanted. It might have a bottom crust, a top crust, or both bottom and top crusts. A traditional pie crust is created with flour, salt, cold water, and lard (or shortening). However, many pie crust recipes call for fats, such as butter, lard, vegetable shortening, or just butter.\nA tart is a sweet or savory dessert with only a bottom crust and shallow edges. Pastry dough (flour, unsalted butter, cold water, and occasionally sugar) makes tart crusts. Tarts are baked in a removable-bottom pan or pastry ring on top of a baking sheet that can be unmolded before eating.\nPies VS Tarts\nThe fundamental distinction between pies and tarts is that pies have an upper crust, whereas tarts do not. While pies appear covered on all sides, tarts are open from the top, allowing you to glimpse the filling. Also, while pies have a thin, silky crust, tarts have a thick, crumbly crust that crumbles when the tart is cut into pieces. Pies are served in the same dish they were prepared, whereas tarts are frequently removed and reshaped if necessary. Finally, pies are harder because of the crust layers at the top and bottom, whereas tarts are more delicate."

"Hello, friends! Today, we’re going to talk about the differences and similarities between pies and tarts including the differences between tart crust and pie crust, what makes a tart a tart and a pie a pie, making pies in tart pans or tarts in pie pans and more.\nThis post is part of my Fundamental Friday series in which I answer your baking and pastry questions. For ease of browsing, you can find all of the Fundamental Friday posts in one place.\nI also invite you to check out my pies and tarts category so you can put what you learn here about what makes a pie a pie, and what makes a tart a tart into action. Thanks for stopping by!\nAccording to Merriam Webster, an American dictionary, here’s what we’re dealing with.\nDefinition of pie: a dessert consisting of a filling (as of fruit or custard) in a pastry shell or topped with pastry or both; a meat dish baked with biscuit or pastry crust\nDefinition of tart: a dish baked in a pastry shell : PIE: such as\na: a small pie or pastry shell without a top containing jelly, custard, or fruit\nb: a small pie made of pastry folded over a filling\nThe Oxford Learner’s Dictionary (The Oxford English Dictionary is only available through libraries and schools/universities) definitions are as follows:\nPie: a baked dish of fruit or meat and/or vegetables with pastry on the bottom, sides and top\nTart: an open pie filled with sweet food such as fruit\nI consulted with my good friend and cookbook author, Jamie Schler, to get the French definitions. She has lived in France since the 1980s and is married to a Frenchman. Thanks for all your help, Jamie!\nHere’s where it gets interesting. Or more interesting. In France, there is no word for what Americans think of as “pie.”\nIn French, the word pie refers either animal coloring (as in piebald) or a bird (as in magpie).\nIn French, there are two words for similar foods with crusts: tarte and tourte.\nA tarte can be sweet or savory, has no sides–so just built on a disc of pastry–or short sides, and no top crust. The term “tarte d l’anglais,” or “English Tarte” is more along the lines of what we’d consider pie: a deeper pastry with a sweet or savory filling enclosed with a pastry top.\nA tourte is also thicker with a top and bottom crust, so I guess in France, a tourte is similar to an American pie, although the connotation is generally that an American pie is sweet and a French tourte is savory (see French Canadian tourtière, or meat pie)\nWhat They Had to Say in Culinary School\nSo, what exactly is the difference between a pie and a tart?\nThis was one of a handful of burning questions that I took with me on my first day of culinary school. On pie v tart lecture day, I craned eagerly forward, waiting for the answer to this pastry mystery.\nGotta tell you, folks–I was in for a bit of a let-down. Turns out, the explanation was….murky.\nHere’s how it went down: “Tarts have short, thick-ish, straight sides. Pies have deeper, thinner, slightly sloped sides. Tart pans look different than pie pans.” This is where I began some serious internal muttering.\n“Pies have flaky crusts, but not all the time. Tarts have sandy, crumbly crusts. Usually. Tarts don’t have a top crust. Pies either do, or they don’t.” Seriously?!\n“Tart crust tastes better than pie crust because it’s an integral part of the dish. The pie crust is just there to hold the filling. Since tarts don’t have a top crust, the fillings are beautifully arranged. Sometimes pies are pretty.” Are you kidding me?!\n“Since tarts have a higher crust to filling ratio, tart fillings are often richer than pie fillings. But not necessarily. And there are always exceptions to any rule. And, why is your face so red, Ms. Field?”\nThe good news is: I neither lunged over the table at her nor cursed exceptionally loudly. The bad news is: I needed more structure than that! I still didn’t know the difference between a pie and a tart after a whole class about it!! Deep breaths….deeeep breaths……..And now, after YEARS of therapy, I have settled down quite a bit.\nA Matter of Degree\nSince there are no hard and fast rules, other than height, my therapist helped me to I see the difference between the two as more of a qualitative one. I also approach it from an American point of view. You know, cuz that’s where I’m from and all.\nSometimes, You Have to Go with Your Gut\nTo me, tarts feel a little more elegant than pies.\nMost pies are homey and comforting, but often good old American pies are all about excess.\nHow many bananas can I cram into that pie? How high can I swirl that meringue? Peanut butter and chocolate and marshmallow cream and toffee pieces? Awesome!\nAmerican big-ass fruit and cream pies are the Hummers of the pastry world. Bigger and richer than they have any right to be, and unapologetic about it.\nRegular American non-steroidal pies are sedans: ample, but not showy; sensible.\nTarts are European sports cars: the perfect marriage of form and function delivered in a relatively small, precision package.\nDifferences Between Tart Dough and Pie Dough\nTart dough is rich, sandy and flavorful, and the fillings are generally made to complement or contrast with the crust nicely.\nFor dessert (sweet) tarts, there are traditionally two types of dough for the crust: either a sable dough, which is sort of like a cookie crust–crumbly and firm, generally sweetened and containing egg.\nThe other option for a French tart dough is a round of puff pastry. In that case, the puff is not sweetened, so all the sweetness would come from the filling.\nAs an aside, old-school French tourtes (with sides), are constructed with a round of puff pastry for the base and a ring of puff pastry around the edges that bakes up to form sides.\nAmerican pie dough can be tasty, but it’s really more about texture than flavor with a pie crust. You either want it to not get soggy, or you want it to be flaky. Flavor is not the main thing–the Thing is that the crust is there in order to give the filling a home and to get the filling to your mouth.\nI like to use a pate brisee for my pie crust. “Brisee” means “broken” in French, and I expect that refers to the butter that’s broken up or rubbed into the flour to make it flaky.\nWhat do the French use this stuff for? I will find out and get back to you. There’s always something sneaking around to muddy the waters of what should be a straightforward discussion!\nThis version of American pie dough uses a combination of shortening and butter to make a crust that contains less water (shortening is 100% fat while butter is about 80-82% fat plus water and milk solids).\nCan You Make a Tart with Pie Crust?\nThe short answer is yes.\nThere are a few things to consider: sable has more flavor than pie crust, so if you want the crust to add its own flavor to the dish, you may want to stick with tart dough.\nSable is also crumbly and sandy (sable is the French word for sand) so will provide a nice contrast to a smooth, creamy filling or to a stewed fruity filling.\nYou can just as easily use puff pastry and rely on all that glorious butter to add flavor.\nCan You Make a Pie with Tart Dough?\nWhile you certainly could make a pie with tart dough, I don’t think I would.\nTart dough really needs to be thicker to hold up, especially the sandy, crumbly sable dough. If you rolled it thinly enough to use as pie crust, I doubt it would hold together.\nAnd using puff pastry to make a pie crust would most likely result in a weird ratio of filling to crust as the puff will puff from the sides in and from the bottom up, leaving not a lot of room for whatever filling you’re planning on using.\nSo, all in all, I’d say it’s a better plan to use pie crust to make a tart than it is to use tart dough to make a pie.\nIf you have questions about this post or recipe, don’t hesitate to get in touch. You can leave a comment on the post and I will get back to you within about 24 hours.\nNOTE: Most of my recipes are written by weight and not volume, even the liquids.\nEven though I try to provide you with volume measurements as well, I encourage you to buy a kitchen scale for ease of measuring, accuracy, and consistency.\nIf you make this recipe and/or have enjoyed or learned from reading this post, I’d appreciate it if you could share this!\nI have Convenient share buttons that float to the left on desk top and on mobile which invite you to share on Pinterest, Facebook, Twitter or Yummly.\nIf you make the recipe, please consider rating it a rating and a review. You can do this via the recipe card in the post.\nReviews really help sell the recipe, and negative reviews help me tune into what people really want to have explained better, so any ratings and reviews are helpful!\nAlso feel free to tag me on Instagram at @onlinepastrychef with #pcorecipe so I can find your creation. Thank you!\nWhile you’re here, I’d love it if you’d sign up for my newsletter. If you like the idea of me occasionally popping into your inbox, here’s how to make that happen:\nWant new and updated recipes to show up in your inbox? Make that happen by clicking here to sign up for my newsletter!\nThanks for spending some time with me today as we mull the differences between pies and tarts. I hope you found the discussion and links helpful.\nTake care, and have a lovely day."

"The Pie Family and All the Cousins:\nPies, Tarts, and Everything in Between (or on top of) Pie Crust\nBy Renee Shelton\n“What is the difference between a pie and a tart?”\nTo answer that and to better understand the differences and similarities between all the pie family members, here are definitions and explanations to many desserts associated with a pie.\nAlso listed are some very old-fashioned recipes from historical cookbooks in my book collection. Titles among my favorite old books: “Little Blue Book No. 1179: How to Make Desserts, Pies and Pastries,” “The Complete Confectioner, Pastry-Cook, and Baker,” “Desserts,” and “The Epicurean.”\nThe Different Types of \"Pie\"\nA pie is a pastry item with a crust and a filling, and can have one or two crusts. Two crusts are often dubbed ‘double crust’ and bottom crust only pie is a ‘single crust. Pies can be sweet or savory, and can be filled with either a cream, fruit, vegetable or meat filling. Often fruit pies have a thickener (flour, cornstarch, tapioca, etc) to help thicken the water and juices released during baking.\nDeep Dish Pie:\nThis is a pie baked in a deep-dish pan (a pie pan with higher sides).\nA tart is very similar to a pie in that it has a pastry dough bottom with a filling. It can have a single crust, or be double-crusted. Often, tarts are thinner than pies. Tart pans are typically fluted around the edges, and can be round, square, rectangular.\nA flan can mean one of two things: an inverted rich egg-based baked custard with a caramel syrup, or an open tart (one crust only on the bottom). The flan related to pies are baked in flan rings, which are metal circles with rolled edges. The pastry dough is laid and pressed inside the ring directly over a sheet pan. A flan shell is simply a plain crust baked alone with the ring. Flan rings come in many different sizes from individual or very large sizes, and can be found in tin, stainless steel or aluminum. A flan (tart) can be savory or sweet.\nFree Form Pie or Tart:\nThis is a pastry dough crust rolled out and instead of placing in a pie tin, it is transferred to a flat baking pan. The center is filled or spread with a filling and the edges are folded around it. The edges can be left as they are or crimped or cut decoratively. It is then baked until the crust is browned and the filling is cooked. Really watery or runny fillings are not good for this as the filling would run over the edges before folding them over. Fruit fillings are excellent for this kind of dessert.\nCroustade / Crostata:\nCrostades or crostatas can be sweet or savory, and is basically anything in an edible container like bread crusts, hollowed rolls, empty pastry shells, cooked mashed potatoes, etc. For pastry, it generally means a free form pie or tart. Croustades can be individual or larger.\nGalettes are sweet or savory baked items. When prepared sweet, galettes can be defined in one of two ways: The first as a round and flat dessert made out of pastry dough, yeast-leavened doughs such as brioche, and even puff pastry, and are often filled with fruits, jams and creams. The second is a round, flat (sometimes crimped) cookie similar to shortbread.\nThese are individual desserts made with pasty dough. Cut out from rounds (or squares or other shapes), turnovers are filled with spoonful or two of filling and folded over. The edges are crimped or pressed to seal. Sweet turnovers are baked or fried.\nThese are similar to turnovers, and are generally fruit-filled. The pastry dough is usually always pie dough, and after frying they are drained and served with a dusting of confectioner’s sugar.\nTarte tatin is a caramelized (classically apple) baked dish with a pastry dough on top. While classically made with apples, tarte tatin can be made with other fruits, especially stone fruits. Sugar is caramelized in an ovenproof pan with butter. Once the sugar is cooked, fruit is added, and it is continued to cook until a deep caramel is formed. The crust is carefully placed over the fruit, and it is baked until the crust is browned. Once it is pulled from the oven, it is inverted on a serving platter, leaving the fruit on top and pastry on bottom. The caramel and resulting syrup from the fruit is served with the dish.\nAn upside down pie is similar to a tarte tatin but with less complexity: just a filling (usually fruit) placed on the bottom of a pan with straight sides for easy unmolding and a crust. Pie crust is placed over the top and the whole thing is baked. It is served inverted on a plate.\nGenerally speaking, these pies have a meringue crust to them. Meringue is spread thickly in a pie pan and baked until it is crisp and dried. Fresh filling is spooned high in the center and served immediately. Cutting this pie is facilitated with a serrated knife. The filling that is often used is a sweetened fruit filling. Some of the popular flavors are raspberry and strawberry since these both contrast nicely with the white meringue crust.\nOrange Meringue Pie\nThis recipe comes from the hard-to-find Little Blue Book collection from the Haldeman-Julius Publications. The book “How to Make Desserts, Pies and Pastries” by Mrs. Temple is No. 1179 in the collection from 1927.\n• 1 cup sugar\n• 1/8 teaspoon salt\n• 1/3 cup flour\n• 1 cup orange juice\n• 1/4 cup lemon juice\n• 1 teaspoon grated orange rind\n• 2 egg yolks, beaten\n• 1 teaspoon butter\n• 2 egg whites\n• 1/8 teaspoon salt\n• 4 tablespoons sugar\n• 1 teaspoon grated orange rind\n1 Pre baked pie crust\nFor the filling: Mix the sugar, salt and flour in the top of a double boiler. Add in juices and cook until thickened, stirring constantly. Add in the egg yolks and butter and cook for another two minutes. Pour into an already cooked pie shell.\nFor the topping: Beat the whites with salt until firm. Add in the sugar and beat until glossy. Fold in the orange rind and top the pie with it. Bake in a moderate oven for about eight minutes until lightly browned.\nGrated Apple Pie\nThis recipe is adapted from a book by Olive M. Hulse. Her book “Desserts: Two Hundred Recipes for Making Desserts Including French Pastries” is loaded with quotes on every page and has a great introduction on “Dessert Lore.” My favorite quote or thought: The discovery of a new dish does more for the happiness of the human race than the discovery of a new planet.\n• 5 large apples, peeled and grated\n• 2 large eggs\n• 4 tablespoons melted butter\n• 1 1/2 cups sugar\n• 1/2 cup cream\n• 1 tablespoon brandy\n• Pinch of cinnamon\n• 2 pie crust shells\nMix all the ingredients together and divide between the two crust shells. Bake until the crusts are browned and the filling is set.\nApricot Flan (Apricot Flawn or Flan d’Abricots)\nThis recipe originally has the flan spelled as ‘flawn.’ \"The Epicurean\" cookbook is 1183 pages of historical menus, culinary definitions and black and white illustrations showing many of the tools and utensils of the chef’s domain from Delmonico’s kitchens from 1862 to 1894. The Epicurean was published in 1920 and written by Charles Ranhofer, ‘former chef of Delmonico’s.’\n• Flan ring, lined with pastry dough\n• Apricots, halved and peeled\n• Superfine sugar, for sprinkling\nArrange the apricot halves in circles, overlapping each other. Sprinkle all over with superfine sugar and bake in a moderate oven until pastry is browned and apricots are softened.\nRemove flan ring, cool and serve."

"Pie crust is the shell which forms the outside of a pie. Old-style pie crusts are made of pastry. They are usually bland, flakey, and somewhat greasy. Many modern pies use crumb crusts, consisting of cookies crumbs or graham cracker crumbs held together with fat. Crumb crusts are generally sweeter and more flavorful than pastry ones.\nThe underside of a pie is always covered. The top may be uncovered (open-topped), fully covered by a crust, or covered by a lattice top crust, which covers some areas while leaving the spaces between the lattices exposed. A non-crust pie topping is a crumb pie topping, which is a rich topping made of loosely blended ingredients, and which, unlike pastry, has little structural integrity."

"Apple pie is only American in the sense that, like the country itself, it is an immigration success story. It had been a traditional treat in Britain and across Europe for centuries, but in the Americas the colonists were lacking one key ingredient: apples. America’s only indigenous apple is the crab apple. Seeds were brought over, and orchards began to spring up, but most of that initial fruit was too tart for eating and was instead made into cider. It took nearly 100 years, as sweeter varieties were being cultivated and as the settlers grew more prosperous, for the apple pie to put down roots as a culinary favorite in the New World.\nThe Uncommon Life"

"|Other Food-related Categories|\n- This article is about Americans as a people. For American, the language, see: American (language)\nThe Apple Pie is a non-American desert served in America which feeds the weaker race and makes them feel special.\nThe food itself originated from Mother Europe which as the name suggests combined the Pastry elements of Pie and the Apple elements of Apple and made Apple Pie. Variations were later made including Apple Crumble, Pumpkin Pie, Citrus Pie, Cheescake and Cream Pie.\nSee Also (Apparently) Edit\n- The Apple Pie of Meats: Meatloaf."

"A pie is a baked dish which is usually made of a pastry dough casing that covers or completely contains a filling of various sweet or savoury ingredients.\nPies are defined by their crusts. A filled pie (also single-crust or bottom-crust), has pastry lining the baking dish, and the filling is placed on top of the pastry but left open. A top-crust pie has the filling in the bottom of the dish and is covered with a pastry or other covering before baking. A two-crust pie has the filling completely enclosed in the pastry shell. Shortcrust pastry is a typical kind of pastry used for pie crusts, but many things can be used, including baking powder biscuits, mashed potatoes, and crumbs."

"- A pie is a baked food, with a baked shell usually made of pastry dough that covers or completely contains a filling of fruit, meat, fish, vegetables, cheeses, creams, chocolate, custards, nuts, or other sweet or savoury ingredients.\n- Pies can be either \"filled\", where a dish is covered by pastry and the filling is placed on top of that, \"top-crust,\" where the filling is placed in a dish and covered with a pastry/potato mash top before baking, or \"two-crust,\" with the filling completely enclosed in the pastry shell.\n- Some pies have only a bottom crust, generally if they have a sweet filling that does not require cooking. These bottom-crust-only pies may be known as tarts or tartlets. An example of a bottom-crust-only pie that is savoury rather than sweet is a quiche.\n- Tarte Tatin is a one-crust fruit pie that is served upside-down, with the crust underneath. Blind-baking is used to develop a crust's crispiness, and keep it from becoming soggy under the burden of a very liquid filling. If the crust of the pie requires much more cooking than the chosen filling, it may also be blind-baked before the filling is added and then only briefly cooked or refrigerated.\n- Pie fillings range in size from tiny bite-size party pies or small tartlets, to single-serve pies and larger pies baked in a dish and eaten by the slice. The type of pastry used depends on the filling. It may be either a butter-rich flaky or puff pastry, a sturdy shortcrust pastry, or, in the case of savoury pies, a hot water crust pastry.\nOccasionally the term pie is used to refer to otherwise unrelated confections containing a sweet or savoury filling, such as Eskimo pie or moon pie.\nA \"cow pie\" refers to cow dung rather than a food.\nMaking Pie Baking Memories\nOne of the fondest memories for many of us, is that smell of baking pies in the oven. To be able to walk in the house and find our mother elbow's deep in baking was a sight to see. The smell of the baked fruit permeated all through the house. To see the kitchen table filled with all the working utensils was so exciting it just made your mouth water.\nPies are one of the most inviting comfort foods that there are and making, baking or eating it can lift our spirits and bring warmth to our every beings. Soothing, soul-satisfying comfort foods can bring back special memories of meaningful moment of the past. Steaming chowders, mashed potatoes, hot soup, hearty stews, warm chocolate chip cookies and fresh baked pies are all foods many of us associate with comfort. They may be simple foods but they evoke fond memories, and bring joy and comfort to our everyday lives.\nHow to make a pie crust: Instruction Video\nHow to make a pie lattice: Instruction Video\nFood & Facts\n- The pies of the Romans, especially at banquets in the days of the empire, were often elaborate concoctions, such as the showpieces in which were enclosed live birds.\n- In England meat and fish pies had become common by the 14th cent., and fruit pies, often called tarts, by the 16th cent. The mince pie was an important feature of the Christmas festivities and was called “superstitious” pie by the Puritans in protest against what seemed to them a pagan manner of celebrating a holy feast. The mincemeat filling was a finely chopped, cooked mixture including raisins, currants, apples, suet, sugar, spice, and often meat, brandy or cider, candied peel, and other ingredients. ~\n- The English settlers in North America retained their taste for pie and adapted it to their new conditions, creating the pumpkin and the cranberry pies.\n- Pie has remained a popular dessert in the United States. In Italy, pie, or pizza, consists, in its most basic form, of a spread of dough covered with tomatoes and mozzarella cheese and baked in an oven.\nSweet Dessert Pies\nSome of these pies are pies in name only, such as the Boston cream pie, which is a cake. Many fruit and berry pies are very similar, varying only the fruit used in filling.\nBanana cream pie\nDutch apple pie\nKey lime pie\nMock apple pie\nPeanut butter pie\nShoofly pie - a pie filled with molasses\nSweet Potato Pie\nBacon and egg pie\nChicken and mushroom pie\nCorned beef pie\nMeat and potato pie\nShepherds' pie (mashed potato crust)\nSteak and ale pie\nSteak and kidney pie\nIf you are a cookbook person, the Internet is full of them!\nHere are a few that we have found.\nCan you name 10 things that you are grateful for today?\nI'm grateful for electric blankets on cold winter nights.\nI'm grateful for new recipes to get my taste buds to watering.\nI'm grateful for birds and squirrels gathering around my feeders.\nI'm grateful for baked potatoes, butter and sour cream.\nI'm grateful for a work from home income.\nI'm grateful for beach dresses and sand between my toes.\nI'm grateful for meat and BBQ sauce cooked on the grill.\nI'm grateful for a house full of cats keeping me cozy at night.\nI'm grateful for Smokey. My gray cuddle bug cat.\nI'm grateful for faith and Gods love."

"A pie is a baked food, with a baked shell usually made of pastry that covers or completely contains a filling of meat, fish, vegetables, fruit, cheeses, creams, chocolate, custards, nuts, or other sweet or savoury ingredients. Pies can be either \"one-crust,\" where the filling is placed in a dish and covered with a pastry/potato mash top before baking, or \"two-crust,\" with the filling completely enclosed in the pastry shell. Some pies have only a bottom crust, generally if they have a sweet filling that does not require cooking. These bottom-crust-only pies may be known as tarts or tartlets. An example of a bottom-crust-only pie that is savoury rather than sweet is a quiche. Tarte Tatin is a one-crust fruit pie that is served upside-down, with the crust underneath. Blind-baking is used to develop a crust's crispiness, and keep it from becoming soggy under the burden of a very liquid filling. If the crust of the pie requires much more cooking than the chosen filling, it may also be blind-baked before the filling is added and then only briefly cooked or refrigerated. Pie fillings range in size from tiny bite-size party pies or small tartlets, to single-serve pies (e.g. a pasty) and larger pies baked in a dish and eaten by the slice. The type of pastry used depends on the filling. It may be either a butter-rich flaky or puff pastry, a sturdy shortcrust pastry, or, in the case of savoury pies, a hot water crust pastry.\nI LIEK PIE\nPIE IS GOOD\nPI IS BAd\nI say the movie about you.\nI think you should have stuck with this practice rather than molesting that pie.\nAn old-time favorite of mine.\nTHE PIE IS A LIE\nMeat pies are good. Banana pies are good. Therefore by extension, a pie containing both meat and banana must be good.\nI've tried it. And no, it does not taste anywhere near good.\nEh, it sounds like it could be alright if you used a plantain, or other not-so-sweet variety of banana.\nPerhaps a beef curry-banana pie would be an ideal choice? Or curry with apples and sultanas in it?\ncoke! thats what i say.\nCoke pie... nice idea! I mean, there is beef and Guinness pie, so there should be banana and Coke pie."

"|Place of origin||United States|\n|Main ingredient(s)||meat (beef, chicken, lamb or turkey), gravy, mixed vegetables (potatoes, carrots, green beans and peas)|\nA pot pie is a mixture of meat pie ingredients made in a pot, hence the name \"pot pie\". It usually consists of flat square noodles and other ingredients such as meat and vegetables. Chicken is a common type. A pot pie is commonly served as a main dish.\nOften confused with pie, a type of baked savory pie with a bottom and top completely encased by flaky crusts and baked inside a pie tin to support its shape, a pot pie is stewed in a pot on top of the stove rather than baked. It lacks a crust. More rarely, some types of pot pies are baked in a deep casserole dish lined with crust but the more common traditional type is crustless. Many food manufacturers and restaurants mistakenly mislabel meat and vegetable pie (e.g., chicken) as \"pot pie\" for marketing purposes to evoke a homemade feel for their food products.\nThe pot pie differs from the Australian meat pie and many British regional variants on pie recipes, which may have a top of flaky pastry, but whose body is usually made from heavier, more mechanically stable shortcrust, hot water crust or similar pastry.\nSome American pie variations have no bottom crust and are similar to a baked casserole (or chicken and dumplings) unlike a traditional meat pie. Since the remaining top crust is not required to offer any structural support, it can be made by closely spacing small dollops of drop biscuit dough onto the stew-like filling before baking. This type of pie is also very common in the United Kingdom, where it is known as a top-crust pie.\nIn the Pennsylvania Dutch region, there is a dish called \"bot boi\" (or \"bott boi\") by Deitsch-speaking natives. Pennsylvania Dutch pot pie is a stew, usually made of a combination of chicken, ham, beef, or wild game with square-cut egg noodles, potatoes, and a stock of onion, celery and parsley. Bouillon is sometimes used to enhance the flavor. The egg noodles are often made from scratch from flour, eggs, salt and water. Some recipes use leavening agents such as baking powder, while others use only flour and hot broth.\n- Longacre, D. J. (1976). More-with-Less Cookbook. Scottdale, PA: Herald Press\n- Hutchinson, R. (1958). The New Pennsylvania Dutch Cookbook. NY: Paperback Library, Inc.\n|This pie or tart-related article is a stub. You can help Wikipedia by expanding it.|"

"Learn something new every day More Info... by email\nCottage pie is a British meat pie made with a beef and gravy filling and a crust of mashed potatoes. It is very similar to shepherd's pie, which has a filling of lamb or mutton with a mashed potato crust. Originally a way to use up leftover roasted meat and cooked potatoes, cottage pie is now often made from raw ingredients. The dish probably dates to the 1700s when the use of potatoes first became widespread in Europe. There are many dishes from other countries that are very similar to both cottage and shepherd's pie.\nTypically, cottage pie is made with beef while shepherd's pie uses lamb or mutton. The recipes are often so similar, that the names are used interchangeably at times. The term \"cottage pie\" appeared earlier in existing written records and dates to the late 1700s. Shepherd's pie was first recorded in the late 1800s, even though experts believe the dish is very likely at least 100 years older than that.\nOlder, traditional recipes using leftovers call for finely dicing the meat and using either leftover gravy to moisten it, or making a new gravy or sauce as a complement. Modern recipes usually use ground beef, called \"minced\" beef in Britain. Some recipes, including one 1894 recipe, include a layer of mashed potatoes on the bottom of the dish, but most recipes only specify an upper crust of potatoes.\nWhether the potatoes are leftovers or cooked just for the cottage pie, they are usually mashed with milk and butter to make them lighter. Other vegetables such as chopped carrots, onions, and celery can either be mixed with the meat or layered on top of it before the topping of potato is spread. Many recipes recommend making the top of the potato crust rough, rather than spreading it smoothly, so the top of the pie browns better. Some also call for drizzling or spreading drippings, melted butter, or beaten egg on top of the potatoes to further aid in browning.\nAnother British meat pie, Cumberland pie, is also very similar to cottage pie. It has a meat filling with a mashed potato layer above that, but adds a layer of mixed bread crumbs and grated cheese on the very top. A North American version adds a layer of canned or creamed corn between the meat and potatoes. Hachis Parmentier, a French dish, uses chopped rather than ground beef, and calls for bouillon rather than gravy. Cheese is mixed into the potatoes in the French pie.\nOne of our editors will review your suggestion and make changes if warranted. Note that depending on the number of suggestions we receive, this can take anywhere from a few hours to a few days. Thank you for helping to improve wiseGEEK!"

"Pies and cobblers are both delicious desserts. Both are also fairly common across the globe, especially in the US and the UK. In spite of their popularity, however, there are still many people who do not know the difference between a pie and a cobbler. If you are one of them, read on. This article will discuss the difference between the two.\n|Has top and bottom crust||Has a top crust|\n|The top crust is made by rolling dough into a thin disc to make sure it covers the entire pie; can also be made by weaving thin strips of dough for a more decorative look||The top crust is made by making small balls of dough and dropping them on the filling; the top crust usually does not cover the entire dish|\n|To make the filling, a thickener should be mixed with the fruit to make sure it does not soak the bottom crust||The use of a thickening agent for the filling is optional because a cobbler only has a top crust|\n|Round; baked in a round pie pan||Can be round, square, or rectangular; can be baked using any baking dish|\nA pie is a baked good that has a crust and a filling. It is usually round shaped and is baked using a round pan with sloping sides.\nThe crust is made by combining flour, water, oil and eggs. The dough is rolled until it becomes a thin disc. The flattened dough will be used to line the bottom of the pie pan and then, the pie filling is placed on the crust.\nThe filling is usually made with fruit and a thickening agent like flour or cornstarch. The fruit can be directly placed onto the pie crust after slicing. However, to make sure its natural juice does not make the crust mushy, the fruit should be coated with cornstarch or flour first.\nSome people also prefer to cook the fruit before placing it onto the crust. To prepare the filling, the fruit should be separated from its juice after cooking. The juice will then be mixed with a thickener. Once cooled, the fruit chunks and juice can be combined again and then placed onto the bottom crust.\nA pie usually has a crust topping which completely covers the fruit filling, although some bakers add a decorative look to the topping by weaving strips of dough. The top crust should be added before the pie is baked.\nOn the other hand, a cobbler is a baked good that has a top crust and a filling without a bottom crust. It can be baked using any baking dish so it can be round, square, or rectangular.\nTo make the cobbler, freshly sliced or cooked fruit is placed in a baking dish with its natural juice or syrup. A thickener or sweetener may also be added to the filling, but it’s usually optional.\nThe top crust can be made with biscuit dough, cookie dough, or even cake batter. Small balls of dough are dropped onto the top of the fruit filling. The crust does not cover the entire pie.\nOnce the pie is baked, the small balls of dough on the top of the pie will look like a cobbled road (hence the name “cobbler”).\nPie vs Cobbler\nWhat, then, is the difference between a pie and a cobbler?\nA pie is typically round, while a cobbler may be round, square, or even rectangular.\nA pie has a top and bottom crust while a cobbler only has a top crust. Adding a thickening agent to the fruit filling is very important in making a pie because the extra fruit juice may cause the bottom crust to become soggy. This is optional, however, when making a cobbler.\nThe top crust of the pie usually covers the entire pie, while the top crust of the cobbler does not. Additionally, the top crust of the pie is made by rolling dough until it becomes a thin disk or by weaving strips of dough, whereas the top crust of the cobbler is made by making small balls of dough and dropping them onto the top of the dish."

"Learn something new every day\nMore Info... by email\nAn apple pie is a pastry dessert which features apples as the star ingredient. There are a number of different styles of apple pie, ranging from traditional closed pies to lattice pies, and this dessert is a ubiquitous offering on the menus of many American diners and casual restaurants. Making apple pies is not limited to Americans, despite the saying “as American as apple pie,” and this dessert is popular in many regions of the world.\nLike other desserts in the pie family, an apple pie consists of a pastry crust and a filling. The crust is traditionally made with flour, shortening, and a small amount of water for lubrication. When well-made, the crust should be light and flaky, with a rich golden color which emerges after baking. Some bakers use more elaborate crusts, including egg crusts, which tend to be more rich. The filling is made by chopping apples and mixing them with seasonings such as sugar, cinnamon, and vanilla.\nAll apple pies have a bottom crust, which lines the pie plate. Some cooks pre-bake the bottom crust to prevent it from getting soggy, while others skip this step. The filling is poured into the crust, and then the pie is topped with a solid crust or lattice. The crust may be decorated with various patterns and designs, and it is traditionally pierced to vent the pie so that it does not burst in the heat of the oven. Some cooks leave their apple pies open, arranging the apples in a decorative design so that the pie is aesthetically interesting.\nThe apples used in pies are typically firm and tart, although softer apples can be used. Cooks may also add other fruits, such as apricots, blackberries, or strawberries, to give the pie more texture and flavor. Apple pie can also be prepared with a custard base, in which case a slice of pie reveals a cross-section of rich custard and apple slices. The seasoning can also vary widely; some cooks make very sweet apple pies, while others prefer heavily spiced versions with cinnamon, cloves, ginger, nutmeg, and just a hint of sugar.\nAlthough people associate apple pie with American culture, the apple pie was invented in Europe. Various apple pastries have been made since at least the Middle Ages, including pies, and the tradition of making apple pie was brought to the Americas by European colonists. North America is an excellent environment for growing apples, which may explain why the apple pie became so popular in the United States.\nan apple pie is a pie that has apple inside that is cut into small pieces.\nOne of our editors will review your suggestion and make changes if warranted. Note that depending on the number of suggestions we receive, this can take anywhere from a few hours to a few days. Thank you for helping to improve wiseGEEK!"

"If you're an American baker, trained on apple pie, hot-water crust pastry flies in the face of just about everything you know about dough. With regular old pie dough, inspired by the French pâte brisée, ingredients should be icy-cold; with hot-water pastry, your butter (or other fat) is fine at whatever temperature as long as it's sort of solid. One ingredient is downright hot—in fact, boiling.\nPie dough requires the judicious sprinkling of (cold, sometimes acidulated) water, and then gentle stirring; with hot-water pastry you just splash some water in and stir vigorously. Pie dough you want to nimbly gather together in your fist and fold over itself a little until everything coheres; hot-water pastry you dump out on the counter and knead the hell out of. Pie dough wants a rest in the refrigerator before it's rolled out; hot-water pastry you can use tout de suite.\nWhat's going on here?\nA bit of pie history: before there was American pie (sweet, fruity, usually dessert), there was British pie—savory, meaty, sometimes made with a variety of animals, including live blackbirds. The word \"pie\" itself is thought to come from the Latin pica, meaning \"magpie,\" and may refer to Brits' hallowed tradition of throwing any old thing between two crusts and calling it dinner, the way magpies and crows collect random detritus.\nWhen Europeans came to the North American continent, the surfeit of land for fruit planting and the nascent sugar-refining industry led to an explosion of dessert pies. As Rachel E. Gross put it last year in Slate, in the U.S. pie has \"come full circle. It started as a way to transform just about any animal into dinner; now it's a way to transform just about any plant into dessert.\" But while it's fine for a modern-day apple pie, for instance, to have a thin, flaky crust—not just fine but ideal—that same kind of crust couldn't do for those earlier meaty British versions: pork pie, veal pie, kidney pie. In those cases something thicker and hardier—but still tender!—was required.\nEnter the hot-water crust pastry, in which fat—lard, shortening, butter, or beef suet, if you're an OG English baker—is emulsified in boiling water as it's incorporated into the flour, meaning this is much more uniform throughout, less flaky, and better able to stand up to chunky or wet fillings than other kinds of pie crust. It's especially good wrapped around free-form pastries like the beef-and-potato pasties I wrote about recently.\nI learned how to make hot-water pastry when I developed the recipe and, as I wrote the other day, found the experience initially disheartening. The recipes I used as a starting point generally credited the pastry as being virtually impossible to mess up, so you can imagine my distress when I messed it up not once, and not twice, but three times. The amount of butter I sacrificed was heartbreaking. Finally on the fourth try I got it right.\nWhat was the problem? I think I was approaching hot-water pastry like I would approach the other kind of pie dough—that is, a bit gingerly. And it was having none of it. It wouldn't roll out without cracking; it wouldn't form around the pasty filling without falling to pieces.\nThe breakthrough came when I let loose. I dumped the water in with abandon, rather than in dribbles. You should too. Does the dough seem at all dry or crumbly? Glug, glug, glug. And I kneaded it well past my comfort zone for kneading pie dough, anxious the entire time. I wish I had watched this Great British Bake Off segment beforehand:\nBecause it turns out some Paul Hollywood panache was exactly what was needed—just a little confident handling. I turned the dough out onto the counter; I positively kneaded it, like you would bread. What resulted, finally, was a soft, pleasantly yellow, slightly greasy-looking mass that I divided into pieces—one for each pasty. This dough doesn't need time to relax, as I mentioned, and can be rolled out immediately. Perfect for these quick-to-come-together pasties, in other words, or if you just can't wait to get that pork-and-egg pie into the oven."

"Mouth-watering crusted dishes, meat pies, and other puffy pastry creations are often thought of when English food is mentioned. The Pithivier, such an enclosed pie, is often used in place of the word pie in English cooking. Some, however, believe that the pie actually originated in the town of Pithiviers, France.\nA Pithivier is typically a dessert pie served with coffee. Fresh fruits, creams, and fillings are often used as its center. Plums and cherries are typical fruits used, while the most popular center is an almond cream filling. Savory cheeses and meats can be used if desired.\nThe distinguishing feature between a Pithiver and a typical pie, aside from the name, can be found on the pie's crust. A tasty caramelized sugar spread is usually basted on the pie as a final cooking step. This shiny glaze can also be accomplished by brushing on an egg wash.\nWhen making a Pithivier, any store-bought puff pastry or puff pastry recipe can be used as the base. The dough should be cut in half, then rolled into two circles that measure eight and one-half inches (21 and one-half centimeters). One circle should be placed on a baking sheet and topped with a cup of almond cream or any other desired filling. Brush an egg wash over the edges of the crust, then place the remaining circle on top. Press the edges together, slit the center of the top circle, and let the pie set for at least one hour in the refrigerator before baking.\nPithivier pies should be baked for 20 minutes in an oven preheated at 350 degrees Fahrenheit (175 degrees Celsius). The result should be a slightly browned crust. To finish the pastry, brush on the shiny glaze and bake for another 15 minutes at 300 degrees Fahrenheit (149 degrees Celsius).\nTo create a simple egg wash for basting the Pithivier crust, combine one quarter of one cup (59 milliliters) of milk, one egg, and two egg yolks. If using traditional almond paste as a filling, buy or make some almond flour. Mix the flour with half of one cup (113 grams) of butter and one egg. A dash of rum may be added if desired. The glaze used in the final step can be made with a simple combination of eggs and sugar or corn syrup to taste.\nDecorative edging is normally incorporated when designing these pies. A knife can be used to create a floral, fluted edging around the pie crust. A visually appealing pattern, such as swirled lines featured all along the top of the pie, can be added as well. These pies are best served while warm and fresh. A serrated knife will ensure the cleanest slices while serving."

"Berries are often referred to as a “superfood” because they are bursting with antioxidants and phytochemicals that are thought to help boost our immune systems.\nDid you know that strawberries have more vitamin C per serving that one orange?\nOr that anthocyanins — flavonoids that are thought to help protect our brains — are what give blackberries their dark, glossy color?\nBlueberries are as good for you as they are plump and delicious. They are packed with phytonutrients — the nutrients that give fruits and vegetables their intense colors and valuable nutritive properties, and that provide health benefits such as cancer prevention. Blueberries are only 80 calories per cup, are a good source of fiber, have virtually no fat and are low in sodium.\nBlueberries can liven up any meal or snack and they complement both sweet and savory dishes. While they can be enjoyed fresh year-round, the peak North American season is April through September.\nTry this recipe for Citrus Crunch Blueberries for another delicious way to enjoy one of nature’s many superfoods. It’s perfect for a quick yet elegant dessert.\nCitrus Crunch Blueberries\n- 2 6-ounce packages fresh blueberries\n- 2 teaspoons orange zest\n- 1 cup fresh-squeezed orange juice (2-4 medium oranges)\n- ¼ cup brown sugar\n- ¼ teaspoon almond extract\n- 2 tablespoons sliced almonds, toasted\nRinse blueberries and divide into four small bowls. Combine orange juice and brown sugar in a small saucepan. Bring to boil over medium heat; cook and stir until thickened. Remove saucepan from heat; add almond extract.\nDrizzle warm syrup over berries. Sprinkle berries with toasted sliced almonds and top with orange zest.\nToasting sliced almonds: Heat sliced almonds in dry, heavy skillet over medium heat 1-2 minutes (until golden brown). Stir or toss sliced almonds frequently for even toasting.\nOrange zest: Wash oranges before zesting. Grate the outermost layer of the orange peel (zest) using a vegetable grater. Try to get as little of the white inner layer of the peel (pith), as it is bitter tasting.\nOrange juice: After zesting the oranges, cut the fruit in half crosswise and squeeze out the juice by hand or use a juicer.\nBerries: To keep your berries their freshest, keep them dry and only wash them right before serving or cooking with them.\nNutrition information per serving: 147 calories, 1.8 grams fat, 6 mg sodium"

"June 25, 2010 > A pie for celebrating healthy eating. And the 4th\nA pie for celebrating healthy eating. And the 4th\nBy Jim Romanoff, For The Associated Press\nHere's a real reason to celebrate - pies don't have to be banned from a healthy diet.\nThe problem with many pies is that they are loaded with excess fat and sugar. The crust usually is the biggest culprit, with up to 220 calories and 15 grams of fat per serving.\nBut the fillings can be trouble as well. Even fruit fillings, which seem healthy enough on the surface, can be hiding more sugar than you think, and sometimes are laced with butter.\nRather than give up your favorite pie, you could take the road of moderation and just enjoy a tiny slice.\nThe other strategy for keeping pie in your diet is to make one you can feel good about indulging in.\nA good place to start is getting rid of the top crust, which immediately lops off a good chunk of fat and calories.\nAs for the filling, fruit is the right idea, just try to limit the sugar. Consider sweetening fillings with fruit juice concentrates or even purees, such as applesauce or apple butter.\nCream and custard pies, which often are made with full-fat dairy thickened with egg yolks, usually can be made lighter with low-fat milk using cornstarch or tapioca as a thickener.\nThis single crust blueberry-peach custard pie uses several of these techniques to produce a more virtuous slice.\nSeveral cups of fresh fruit are baked into a light custard made with only two whole eggs, skim milk and nonfat Greek-style yogurt, which adds body and a hint of tanginess that balances the natural sweetness of the peaches and blueberries.\nBLUEBERRY-PEACH CUSTARD PIE\nStart to finish: 3 hours (15 minutes active)\n1 cup sugar\n3/4 cup skim milk\n3/4 cup (6 ounces) nonfat plain Greek-style yogurt\n2 large eggs\n2 tablespoons all-purpose flour\n2 teaspoons cornstarch\n1/4 teaspoon almond extract\nPinch of salt\n1 store-bought, refrigerated pie crust\n1 cup blueberries\n1 cup peeled, sliced peaches\nPosition a rack in lower third of the oven. Heat the oven to 400 F. Coat a 9-inch pie pan with cooking spray.\nTo make the filling, in a medium bowl, combine the sugar, milk, yogurt, eggs, flour, cornstarch, almond extract and salt. Whisk until smooth. Set aside.\nOn a lightly floured surface, roll a sheet of pie crust into a 12-inch circle. Place the crust in the pie pan and trim so it overhangs evenly by about 1-inch. Fold the edges under and crimp or flute the edge with your fingers or a fork. Place the pie pan on a baking sheet.\nArrange peaches in the bottom of the crust and top with the blueberries in an even layer. Pour the filling on top (the fruit will float but this won't affect the final results). Bake for 25 minutes.\nAfter the pie has baked for 25 minutes and the filling is beginning to set, remove from oven and cover the edges of the crust with foil to help prevent over browning. Reduce heat to 350 F and return the pie to oven.\nBake until a knife inserted at the center of the pie comes out clean, another 20 to 25 minutes (the pie may puff up quite a bit but will settle during cooling). Let cool for 1 1/2 hours. Serve warm or refrigerate until cold and serve chilled.\nNutrition information per serving (values are rounded to the nearest whole number): 200 calories; 58 calories from fat; 6 g fat (3 g saturated; 0 g trans fats); 41 mg cholesterol; 34 g carbohydrate; 4 g protein; 1 g fiber; 163 mg sodium."

"Types of Pies\nFire up the oven! It's that time of year that we start thinking about baking again. Here's a crash-course in the basic types of pies – and what makes them wonderful.\nLearn the differences among all the many delicious types of pies break down to their crusts and fillings.\nCome on -- let's BAKE!\nPies can be single-crust or double-crust. A single-crust pie is also known as an open pie as it only has a crust in the pie dish containing the filling, but no crust on top sealing it all in.\nA double-crust pie, or a closed pie, has the same bottom crust as an open or single-crust pie and a second crust covering the top. The top crust on a double crust pie is typically cut in a few places to vent air through as the pie cooks.\nAn alternative to this is to weave strips of pie crust dough into a latticework over the top, creating an attractive sort of checkerboard pattern that leaves plenty of venting room and reveals the mouth-watering colors of the filling contained inside.\nA typical pie crust is made from white, all-purpose or pastry flour. But it's also not uncommon to see pies with a whole wheat crust, graham cracker crust or even a cornmeal crust. You can also add dry ingredients such as chopped nuts (like pecans or walnuts) or seeds (like caraway or poppy) and spices (like cinnamon, cloves or nutmeg) to your pie crusts for additional richness in texture and flavor.\nTo most pie lovers, a pie is defined by its filling. Fruit pies are among the most familiar, with apple pie at the pinnacle, though you'll also find strawberry, rhubarb, cherry, peach and a different berry pie for every variety of berry.\nFruit pies can be made with fresh fruit or with frozen, canned or even glazed fruit. Certain vegetables also lend themselves to delicious sweet pies, perhaps most notably pumpkin pie.\nVariations on the basic fruit pie include fruit cream pies, like banana cream pie, and fruit custard pies, like lemon meringue. The meringue in lemon meringue pie is a foamy mixture of sugar, butter and eggs piled over the filling in place of a standard top crust. Key lime pie is similar in design to lemon meringue except, of course, without the meringue. Both lemon and lime pies can also be made as chiffon pies, which has an even lighter, fluffier texture than regular cream pies due to the marshmallow, whipped cream or beaten egg whites in the ingredients.\nOther creamy, custardy pies include chocolate cream pie, coconut cream pie, Boston cream pie and Bavarian cream pie. Less commonly, you may also find vanilla cream and butterscotch cream pies. Pies may also have alcohol like rum or bourbon in the ingredients, such as the popular Grasshopper pie, a chocolate mint pie containing crème de menthe served in an Oreo cookie shell.\nCertain cultures are known for their trademark pies, such as mince pie (or mincemeat pie), a British Christmas tradition literally containing minced meat mixed with spices, and Whoopie pies, recently named the official dessert of the state of Maine (what? not blueberry pie?) containing a creamy, frosting-type filling wedged between two large cake-like chocolate or pumpkin cookies.\nAll the pies mentioned so far are sweet pies, or dessert pies, but savory pies are also popular, including pot pies which contain a mixture of meat and vegetables, typically cooked and served in individually sized double crusts. Shepherd's pie is another common savory pie that has no lower crust, only an upper crust made of a mashed potato mixture.\nOnce prepared, pies can be served frozen (like ice cream pies), refrigerated (like cream and custard pies), or warm (like fruit pies or savory pot pies).\nPies to Die For\nStep outside the box and try a type of pie you've never tried before!\nWant to browse more pies to try? Check out our collection of Easy Pie Recipes\nMmm, pie. What's your favorite?"

"The essentials of baking pies and tarts\nThe challenge in making pies and tarts is to cook two very different materials-a barely moist dough and a wet filling-so that the dough ends up very dry and crisp and the filling thick and moist.\nFor a crust that best resists sogginess from wet fillings, choose a crumbly crust made with egg. Flaky crusts more readily soak up liquid.\nTo make sure that the crust won't be undercooked and to minimize sogginess, prebake the crust in the pan \"blind,\" without filling. Line the crust with parchment paper and weigh it down with dry beans or ceramic pie weights for part of the prebaking. When weights are removed, \"dock\" the dough by pressing down with fork tines to prevent blistering. Protect exposed edges from excess heat with strips of kitchen foil or pie guards.\nGive the prebaked crust a moisture-resistant coating of beaten egg, chocolate, melted butter, concentrated fruit preserves, or pastry cream, or a layer of moisture-absorbent crumbs. For an egg wash, return the crust to the oven for a few minutes until the coating is dry, then let it cool before filling and baking.\nFresh fruit fillings often release copious liquid and fail to thicken well, especially if the fruit has been sliced.\nTo control the consistency of a fresh fruit filling, concentrate and thicken the juices before baking. Cut the fruit, toss it with sugar in a colander, and let the juices drain into a bowl. Cook down the juices until thick, recombine them with the fruit and thickener, and fill the crust.\nFor a translucent fruit filling, thicken the fruit juices with tapioca instead of flour or cornstarch.\nBake fruit pies or tarts near the oven floor, or directly on a baking stone on the floor, to ensure rapid heating of the bottom crust.\nCream and custard pie fillings may fail to thicken in the oven, or may thicken well but then reliquefy.\nFor cream and custard fillings thickened with eggs and flour or starch, be sure to heat the flour-egg mixture to 180 to 190°F / 80 to 85°C, either before or during baking. Undercooked egg yolks contain an enzyme that breaks down starch and liquefies fillings.\nQuiche fillings are easily overcooked and dried out.\nCheck quiches frequently during baking and remove from the oven as soon as a toothpick or knife tip inserted in the center comes out clean.\nAllow quiches to cool until the custard is firm enough to cut without slumping.\nLemon meringue pies often weep liquid from the meringue surface or the bottom, where it floats the meringue from the filling.\nMake a stable meringue topping by using powdered sugar that includes cornstarch and placing the meringue on a lemon filling that's still hot. Or make a precooked meringue on the stove top, then place on the pie and finish it in the oven to warm it through and brown the edges.\nEnsure a stable lemon filling by cooking the cornstarch-sugar-egg mixture to 180 to 190°F / 80 to 85°C, and adding the lemon juice afterward off the heat.\nKEYS TO GOOD COOKING provides simple statements of fact and advice, along with brief explanations that help cooks understand why, and apply that understanding to other situations. Not a cookbook, Keys to Good Cooking is, simply put, a book about how to cook well.\nExcerpted from Keys to Good Cooking by Harold McGee Copyright © 2010 by Harold McGee. Excerpted by permission of Doubleday Canada, a division of Random House of Canada Limited. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher."

"A flawlessly prepared pie dough is a thing of beauty. Pie crust should hold together enough to contain the filling, yet be flaky and crumbly to the bite.\nUsed for both sweet and savory preparations, once you’ve mastered the techniques for creating good crusts and delicious fillings, you can get as creative as you like – your only limit is your imagination!\nUnderstanding the basics of Baking & Pastry and the differences between pie dough and filling preparations will ensure that you get the perfect pie each time. Here are a few points to note:\n- Pastry flour is the best choice of flour for pie dough because of its medium gluten content\n- Shortening is the most popular fat used due to high melting point, cost and flaky result. However, as butter tastes better, many recipes combine fats.\n- Water is added for gluten development. Too much though, it becomes tough. Too little, crust falls apart.\n- Salt’s contribution is flavor\n- THE MOST IMPORTANT NOTE: dough and ingredients need to be kept COLD – gluten develops more slowly in cold\nVARIATIONS OF PIE DOUGH:\n- FLAKY – fat is incorporated into flour by cutting it in until it is the size of peas\n- MEALY – fat is blended into flour more thoroughly until it looks like coarse cornmeal – crust is short and tender because less gluten develops (as less water is used, this dough is best used for the bottom of a pie because it can absorb more moisture)\n- CRUMB CRUSTS – only used for unbaked pies i.e. graham cracker crust; pre-bake the crust prior to adding the filling\nThickeners such as cornstarch, gelatin and waxy maize (for freezing) are combined with other ingredients to create the texture needed for pie fillings.\nFruit fillings can be prepared three ways:\n- Cooked Fruit Method – the actual fruit is cooked in a pot and then placed in the crust (best for hard fruit)\n- Cooked Juice Method – the fruit is strained and its juice is cooked and thickened before adding the fruit to the crust (best for frozen or canned fruit)\n- Old-Fashioned Method – the fruit is peeled and cooked in the pie\nCustard or Soft Fillings rely on the coagulation of eggs\nChiffon Fillings are made by adding gelatin to a cream filling or fruit filling and folding in egg whites and/or whipped cream\nFor one of my favorite basic pie crusts, check out Martha Stewart’s recipe.\nAnd definitely try my recipe for this savory pie – Tarte a L’Oignon."

"The fondest memory I have from my childhood is one that I hold dear to my heart. Fitted with an over-sized apron and a smile from ear to ear, I was six years old on a stool rolling out pie pastry along side my Mom. While she made the large pies for the family, I rolled out pastry for miniature imitations formed to the confines of empty, metal chip-dip containers. I was very proud and happy to be a part of the preparation for such a wonderful treat.\nPies are a very traditional way to end a meal on certain holidays throughout the year, and especially at Christmas time. Pumpkin is always a favourite pie among many for the holidays, but numerous different pies can and will be made and enjoyed.\nPies are basically made up of a shell or crust, with a flavourful filling, and can be divided into two groups: baked or unbaked. Baked pies are obviously ones with raw pie shells that are filled and then baked. The unbaked category represents prebaked pie shells that are filled with a prepared filling and then chilled to set before serving.\nThe pie dough that makes up these shells can also be divided into two categories: flaky dough or mealy dough. Flaky dough is usually a pastry that has a mixture of shortening and butter that is “cut in” so that there are small chunks still left in the finished product. This aids in creating steam, which helps with the leavening process and thus creating the flaky texture. Mealy dough is one that is usually made with butter that is mixed in more thoroughly, and when baked has a texture much like tender shortbread. This is because the flour particles are more coated with fat and thus less gluten is formed.\nOnce you have decided on the type of crust to make, it is time to decide on the filling. Basically there are four choices: fruit, custard, cream, or chiffon. All fillings require the existence of a starch or stabilizer to ensure that it holds together when sliced. Fruit and cream fillings use starches, such as cornstarch for their stability, while custard filling use the stabilization of eggs coagulation for their firmness. Examples of custard pies are ones such as pumpkin, pecan, and key lime pies. Chiffon pies usually use a combination of starch or gelatin with whipped eggs whites folded in.\nBaking is a science and recipes are the formulas. For the reasons listed here and for many others, it is important to follow these recipes exactly in order to have a successful outcome. Whatever pie or other dessert you choose to finish your holiday meals with, I wish you, your families, friends, and loved ones all the best in health and happiness this upcoming holiday season.\nDear Chef Dez:\nI have heard and known that it is best to keep pie pastry as cold possible to prevent melting the butter and shortening pieces. What is the best way of doing this?\nDouglas C., Langley\nThe best way of doing this is to first focus on your ingredients. Make sure you are using ice water instead of cold water, and frozen butter grated into the flour mixture is ideal. The frozen butter particles then are already the required size from the grater and will not suffer from the warm friction of too much mixing or “cutting” it in.\nSecondly, try not to touch the dough with your hands, as the warmth from them will melt the butter. It is best to form the dough by folding it over consistently with a metal dough cutter (bench scraper).\nOnce the dough is formed, wrap and place it in the refrigerator until thoroughly chilled. Remove and proceed with rolling, ideally on a chilled marble surface. Once shaped, refrigerate for approximately 10 more minutes before baking.\nI have even heard that using vodka from the freezer (instead of the ice water in your recipe) will produce a flakier crust."

"New research published in the BMJ suggests that for positional skull deformation in infants - flattening of the skull as a result of laying in the same position for long periods - wearing a corrective helmet does not improve the condition.\nIt is unknown as to how many infants in the US experience positional skull deformation, also known as flat head syndrome. In the UK, it is estimated to affect 1 in 5 babies under the age of 6 months.\nThere are two types of positional skull deformation - plagiocephaly and brachycephaly. Plagiocephaly occurs when one side of the head becomes flat, causing the infant's ears to become misaligned. Brachycephaly is when flattening occurs on the back of the head, causing the front of an infant's skull to bulge.\nSince the skulls of young infants are very soft, constant pressure on a specific area of their head can cause it to change shape. This is what happens in positional skull deformation. It is mainly caused by a baby's sleeping position.\nPast studies have shown that since the launch of the American Academy of Pediatric's (AAP) \"Back to Sleep\" campaign in 1992 - which recommends that parents should position babies on their backs when sleeping to reduce the risk of sudden infant death syndrome (SIDS) - there has been a dramatic increase in the number of children affected by positional skull deformation.\nResearchers say that use of a corrective helmet for infant positional skull deformation should be \"discouraged\" as it has \"no benefits.\"\nIn most cases, a baby's skull will correct itself over time. But in more severe cases, treatment may be required. This may involve the use of helmets, known as cranial orthoses.\nThe idea is that the helmets stop the infant lying on the flattened area of their head. Treatment is usually started when the infant is 5 or 6 months old - when their skull is still soft enough to be moulded. The helmet is required to be worn up to 23 hours a day, and full treatment usually takes around 3-6 months.\nBut in this latest study, researchers from the Netherlands have questioned the benefits of such treatment.\nAccording to the team, there has been little research comparing helmet therapy in infants with flat head syndrome with no treatment. Therefore, they set out to do just that.\nUse of a helmet as standard therapy 'discouraged'\nFor their research, they assessed 84 babies who had moderate or severe positional skull deformation. They had either plagiocephaly or brachycephaly.\nFrom the age of 6 months, half of the infants were required to wear custom-made closely fitting helmets for 23 hours a day for a 6-month period. The remaining infants had no treatment at all.\nOn measuring the head shape of all infants once the babies reached 2 years old, the team found that the infants who wore the helmets showed no significant improvements, compared with those who received no treatment.\nHelmet therapy led to 25.6% of infants making a full recovery from positional skull deformation, while 22.5% of infants who received no treatment made a full recovery - which the researchers deem as \"no significant difference\" between groups.\nSide effects were reported by parents of the infants who wore the helmets. Around 96% of parents said their babies experienced skin irritation and 33% said they experienced pain. Approximately 77% of parents felt the helmet prevented them from cuddling their infants, 76% reported an unpleasant smell and 71% reported sweating.\nWhen the infants were 2 years old, the researchers found that both groups of parents were generally happy with the shape of their child's head. The parents of those who wore the helmets reported a satisfaction score of 4.6 out of 5, while parents of children who received no treatment reported a satisfaction score of 4.4 out of 5.\nFurthermore, the team notes the high costs of helmet therapy. On average, they found that the treatment cost around $1,935 (£1,157) per child.\nCommenting on their findings, the researchers say:\n\"Based on the equal effectiveness of helmet therapy and skull deformation following its natural course, high prevalence of side effects, and high costs associated with helmet therapy, we discourage the use of a helmet as a standard treatment for healthy infants with moderate to severe skull deformation.\"\nThe researchers point out that in both groups, only 25% of babies made a full recovery. Therefore, they stress the importance of preventing babies from developing positional skull deformation.\nThey note that past research has indicated that babies should be placed on their tummy while awake. But they emphasize that while a baby is sleeping, the AAP guidelines - recommending that babies should be positioned on their back - should be followed.\nIn an editorial linked to the study, Prof. Brent R. Collett, of the University of Washington School of Medicine, says that it is important that parents are aware of the implications of helmet therapy and that future research involving larger samples of children would be useful to investigate further.\n\"In particular,\" he adds, \"it would be of interest to learn whether children with the most severe positional plagiocephaly and brachycephaly, who were excluded from this trial, show meaningful improvement.\"\nWritten by Honor Whiteman"

"If you thought that a helmet can save you from the dreadful brain hemorrhages, then you might have to revisit that thought. Helmets, which are known for incarcerating and thus protecting your skull, might as well cause a rotational injury. Philips took the pains of providing us with helmets which can reduce the risk of any kind of brain hemorrhage by 70%.\nIntracerebral shearing, commonly known as rotational injury happens during accidents when the head ( with the helmet on) hits the road and because of the smooth outer texture of the helmets, it rotates, The whole process is so fast that it can cause the rupturing of the cranial nerves. Thus, Philips came up with the idea of covering the outer shell of helmets with a membrane, a SuperSkin®!\nSuperSkin® is a highly elastic yet strong membrane, which is made to withstand any kind of stress and strain! Louis Pasteur University of Strasbourg put this theory to test and they now believe that helmets with this technology can reduce the chances of rotational injury by 67.5%.� The SuperSkin® will not cost you more than 150 euros, as far as safety is concerned, there is no price to it."