ejaasaari/simplewiki-2025-04-01 huggingface dataset:
Euler's identity, sometimes called Euler's equation, is this equation: formula_1 It features the following mathematical constants: It also features three of the basic mathematical operations: addition, multiplication and exponentiation. Euler's identity is named after the Swiss mathematician Leonard Euler. It is not clear that he invented it himself. Respondents to a "Physics World" poll called the identity "the most profound mathematical statement ever written", "uncanny and sublime", "filled with cosmic beauty" and "mind-blowing". Mathematical proof of Euler's Identity using Taylor Series. Many equations can be written as a series of terms added together. This is called a Taylor series. The exponential function formula_8 can be written as the Taylor series formula_9 As well, the sine function can be written as formula_10 and cosine as formula_11 Here, we see a pattern take form. formula_12 seems to be a sum of sine and cosine's Taylor series, except with all of the signs changed to positive. The identity we are actually proving is formula_13. So, on the left side is formula_14, whose Taylor series is formula_15 We can see a pattern here, that every second term is "i" times sine's terms, and that the other terms are cosine's terms. On the right side is formula_16, whose Taylor series is the Taylor series of cosine, plus "i" times the Taylor series of sine, which can be shown as: formula_17 if we add these together, we have formula_15 Therefore, formula_13 Now, if we replace x with formula_2, we have: formula_21 Since we know that formula_22 and formula_23, we have: which is the statement of Euler's identity.
Hideki Tōjō (30 December 1884 – 23 December 1948) was the Prime Minister of Japan during most of World War II. Hideki Tōjō was born on 30 December 1884 in Tokyo, Japan. He was the third son of a lieutenant general in the Imperial Japanese Army named Hidenori Tōjō. Tōjō had two older brothers but they died before he was born.  In 1909, he married a woman named Katsuko Ito and he had seven children with her: three sons and four daughters. In the late 1930s, Hideki Tōjō fought in the Second Sino-Japanese War, leading Japanese forces in occupied Manchuria. He returned to Tokyo in 1940 and held ministerial posts, where he urged an alliance with Germany and Italy against the Allied forces. Tojo became Prime Minister in 1941 and within two months ordered a surprise attack on Pearl Harbor planned by Admiral Isoroku Yamamoto. He followed it with a declaration of war against the United States, Britain, and the Netherlands.  After Japan surrendered, American troops went to arrest Tojo and surrounded his house. He shot himself four times in the chest, but missed and the bullets hit his stomach. Disarmed and with blood gushing out of his chest, Tojo began to talk. He said, "I am very sorry it is taking me so long to die. The Greater East Asia War was justified and righteous. I am very sorry for the nation and all the races of the Greater Asiatic powers. I wait for the righteous judgment of history. I wished to commit suicide but sometimes that fails."  After his injuries healed, the Allies found Tojo guilty of war crimes and hanged him in Tokyo on 23 December 1948.
SUSE is a main version of a Linux distribution, produced in Germany and owned by Attachmate Group. SUSE is also a founding member of the Desktop Linux Consortium. Starting from version "10.2 Alpha 3" its official name is openSUSE. The current mascot of SUSE is a chameleon called "Geeko". History. The SUSE Linux distribution was originally a German translation of Slackware Linux. The Slackware distribution was founded by Peter MacDonald, and was the first distribution to contain X and TCP/IP. S.u.S.E was founded in 1992 as a UNIX speaking group, which among other things regularly released software packages that included SLS and Slackware, and printed UNIX/Linux manuals. In 1994 the group released the first CD version of SLS/Slackware, under the name "S.u.S.E Linux 1.0." Then in 1996, SuSE Linux gained many aspects from Red Hat Linux. The name "SUSE Linux" came in September 2003. On 4 November 2003, Novell announced it would buy SuSE. They planned to release the administration program YaST2 under the GPL license and add a community project, openSUSE. The openSUSE desktop environment can be GNOME or KDE. Most parts of the program were "open"—not completely, but more than before. The version "10.0" was the first version that had public beta testing. The philosophy changed from before. There were multiple versions of the "10.0" Linux distribution for download. They are "OSS" (completely open source), with all programs "free" and without proprietary softwares, and "eval" (has both open source and proprietary applications).
Laissez-faire is an economic and political philosophy. It is from a French phrase that means to "leave alone". It means that government does not interfere with business and economy. Finance and trade decisions are left for the private individual to make. It is the belief that unregulated competition in business represents the best path to progress. Supporters claim that a free and unregulated market creates a natural balance between supply and demand. The phrase is supposed to have come from the 18th century. In a meeting between the French finance minister Colbert and a businessman named Le Gendre, Colbert asked how the government could help commerce. Le Gendre replied "Let us do what we want to do". History. In Ancient China, there were three schools of political thought. Taoism believed in almost no economic interference by the government. Legalism included the belief that the state should have the maximum power. They created the traditional Chinese bureaucratic empire. Confucianism was split between these two extremes although was closer to Legalism than Taoism.  During the 19th century Laissez faire developed as a social and economic philosophy. It was believed that government involvement in business was harmful at worst and ineffective at best. Socially, it was believed that government intervention to help the poor was harmful because it made them lazy and dependent on the government. Economically there was debate at this time in Europe and the United States over whether free trade or tariffs promoted the most economic growth. Up until the 1840s protectionism was favored over Laissez faire. In Britain the Corn Laws placed high tariffs on imported corn to protect British farmers and land owners.
Dorothy Marie "Dottie" Metcalf-Lindenburger (born on May 2, 1975 in Colorado Springs, Colorado) is an American astronaut. She works for NASA. She is married to Jason Metcalf-Lindenburger, who was a 7th grade school teacher at the time. NASA experience. Metcalf-Lindenburger was selected by NASA in May 2004 and began training. Astronaut Candidate Training includes tours, many scientific and technical meetings, much learning about the Shuttle and International Space Station systems, physiological training, T-38 flight training, and water and wilderness survival training.  She successfully finished this training in February 2006. This qualified her as a NASA Astronaut.
A worker is a person who does a job. This usually means a person who does manual labour, like manufacturing goods. In economics there are three factors of production. These are "labour" (the work done by workers), land (usually people need some space to produce something), and capital (it will cost resources, or money, to produce something).. People who work, usually get paid for the work they do. This is either called wages (if it is bound to a time period, like an hour), or a salary (if it is independent of the time taken).  May Day is an international holiday for workers' rights.
Actinium is chemical element 89 on the periodic table. Its symbol is Ac. Actinium's mass is 227 g/mol.  Actinium is a silver radioactive, solid metal in actinide group. It is so radioactive that it glows in the dark. Even a small amount of actinium is dangerous to people. History. Actinium was discovered in 1899 by André-Louis Debierne, a French chemist. In 1899, Debierne described the substance as similar to titanium and (in 1900) as similar to thorium. Properties. Actinium is a soft, silvery-white, radioactive metal. Its estimated shear modulus is similar to that of lead. Because its strong radioactivity, actinium glows in the dark with a pale blue light. Actinium reacts quickly with oxygen and moisture in air forming a white coating of actinium oxide that stops the actinium from oxidizing. Isotopes. Actinium that is found in nature is made up of two radionuclides 227Ac and 228Ac. Thirty-six radionuclides of actinium have been found. The most stable is 227Ac which has a half-life of 21.772 years. The shortest-lived known isotope of actinium is 217Ac which has a half-life of 69 nanoseconds. Occurence. Actinium is only found in trace amounts in uranium ores. For example, one tonne of uranium ore contains about 0.2 milligrams of 227Ac. Thorium ores contain about 5 nanograms of 228Ac per one tonne of thorium. Uses. 225Ac is now being studied for use in cancer treatments. 227Ac is studied for use as an active element of radioisotope thermoelectric generators. 225Ac is used in medicine to make 213Bi in a reusable generator. It can be used in radiation therapy.
Alyson Renee "Aly" Michalka (born March 25, 1989) is an American actress and musician. She works with Disney Channel and takes part in duo group 78violet with her sister, Amanda Michalka. She is most well known for playing the part of Keely Teslow on the Disney series Phil of the Future. Early life. Alyson Michalka was born in Torrance, California, United States on March 25, 1989 to Mark Michalka and Carrie Begley-Michalka. She was raised mostly in the city of Seattle, Washington. She has two dogs named Saint and Bandit. Later life. She began to be home schooled. She started acting for Disney Channel on "Phil of the Future", then began her singing career. She says on "Disney 411" that she started playing guitar with her sister at the ages of 12 and 10. She lives in a multimillion-dollar California mansion. Musical career. Michalka has been singing since her sister was able to speak and sing. Then, for the movie "Now You See It..." her sister and she started a band and created a music video called "Do You Believe In Magic?". The band is called 78violet. Then they left Disney Channel to "take off" with their musical career. Acting career. Soon she started acting for Disney Channel in the show "Phil of the Future", which she had quit in 2006. She has been seen in many movies, outside of Disney channel, she worked with WB and NBC with TV dramas with her sister. She was most known for playing "Keely Teslow" in "Phil of the Future" on Disney Channel, though now has gained popularity being in a band. She has been in other Disney Channel productions like "Now You See It..." and "Cow Belles". She is half of the musical duo 78violet, with her sister.
Brenda Song (born March 27, 1988) is an American actress. She is also a former child model. Song was first famous for her appearances on the Disney Channel. She was a regular part on "The Suite Life of Zack and Cody". Her character was noted as one of the Disney Channel's longest continuous characters. In 2010, she moved into mainstream movies and TV. These included "Changeland", "Angry Angel", and "Station 19". Biography. Early years. Brenda Song was born in Carmichael, California to a Hmong American father and a Thai American mother. Song has two younger brothers, Timmy and Nathan. Brenda Song holds a black belt in Taekwondo and was named an All-American Scholar in ninth grade. Career. Brenda Song began acting and modeling at age 6. She also played a very minor role in a skit on MADtv. One of Song's more notable acting roles is her portrayal of London Tipton in the Disney Channel Original Series "The Suite Life of Zack and Cody" (along with Ashley Tisdale and twins Cole and Dylan Sprouse). She later continued this role in the spin-off "The Suite Life on Deck". She also played a recurring role as Tia in the Disney Channel Original Series "Phil of the Future". Song had minor guest appearances on both "That's So Raven" and ". Song had her first starring role in 2006 in the movie ". In 2010, Song was part of the main cast of "The Social Network". This marked her entry into mainstream movies and TV. In 2012, Song starred in the short film "First Kiss" along with her "Social Network" costar Joseph Mazzello. In 2017, Song was cast in Freeform's movie, "Angry Angel". In January 2019, Song was cast in a starring role in the Hulu television series "Dollface" alongside Kat Dennings. Personal. She has received a black belt in one martial arts and had used her skills in the Disney Channel movie, "". In 2017, Song began a relationship with actor Macaulay Culkin. They have a son together named Dakota, born in 2021.
Guide dogs are dogs trained to help blind or vision impaired people live on their own. They are sometimes called "Seeing Eye" dogs. Guide dogs are one type of assistance animals, which are animals trained to help people with a disability to lead more complete lives. The blind person (sometimes called a "handler") and the dog need to work together. Both the dog and the handler must take special training to learn how to work as a team. The handler needs to let the guide dog know the direction they want to go. The dog can lead the person around things that may be dangerous, such as moving cars or other things. Also, guide dogs may be taught to press buttons to work elevators or get things for their handler. Because dogs cannot see colors as well as people, they cannot read traffic signals, so the handler must use ways to tell if it is safe to cross a street. Because the guide dog and handler will be in public, it is important that the dog stays calm in busy or loud areas. In many countries, guide dogs are allowed inside places where animals normally are not allowed, such as restaurants, stores, buses and trains. History. Germany started the first guide dog schools during World War 1, to help soldiers who were blinded in the war. By 1931, schools and organizations such as The Seeing Eye in Morristown, New Jersey in the United States and the British Guide Dog Association in the United Kingdom were founded.
Keelung (; Hokkien POJ: '), officially known as Keelung City"', is a provincial city of Taiwan Province, Republic of China. It is in the northeastern part of the island. It is next to Taipei County. Nicknamed the "Rainy Port" for its frequent rain and maritime role, the city is Taiwan's second largest seaport (after Kaohsiung).  History. Early History. Keelung was first inhabited by the Ketagalan, a tribe of Taiwanese aborigine. The Spanish expedition to Formosa in the early 17th century was its first contact with the West; by 1624 the Spanish had built , a fort in Keelung serving as an outpost of the Manila-based Spanish East Indies. The Spanish ruled it as a part of Spanish Formosa. From 1642 to 1661 and 1663–1668, Keelung was under Dutch control. The Dutch East India Company took over the Spanish Fort San Salvador at Santissima Trinidad. International relations. Twin towns – Sister cities. Keelung is twinned with:
A chocolate cake is a cake made with chocolate or cocoa. The ingredients are put into a bowl and mixed together; then the mixed ingredients are put into a cake tin and put in an oven until it is fully cooked. Then the cake is taken out of the oven and placed on a cooling stand. If the cake maker wants to, they can ice the cake, when it has cooled down, by spreading thick icing on it. Chocolate cakes are sold in shops as well as made at home. They are a sweet food and should not be eaten all the time, which would be unhealthy. There are many different types of chocolate cake, depending on the recipe and different types of chocolate used. Different countries have different recipes for chocolate cakes. In France, "gâteau au chocolate" is popular. In Germany, "Sachertorte" is popular. History. In 1828 Conrad Van Houten of the Netherlands made a mechanical extraction method for taking away the fat from cacao liquor resulting in cacao butter and the mostly de-fatted cacao. It was a compacted mass of solids that could be sold as it was "rock cacao" or ground into powder. The processes made chocolate from an luxury to an cheap daily snack. A process for making smoother chocolate called conching was made in 1879 by Swiss Rodolphe and made it easier to bake with chocolate as it ""amalgamates smoothly and completely with cake batters"." Until 1890 to 1900 chocolate recipes were mostly for drinks. In the U.S., chocolate decadence cakes were popular in the 1980s; in the 1990s, single-serve chocolate cakes with liquid chocolate centers were popular.
Ten Who Dared is a movie made by Disney in 1960. It tells the real story of an officer of the United States Army called John Wesley Powell who was the first to travel up the Colorado river with other nine men to make a map of the region, and the dangers they had to face in their trip. Some people say it is one of the worst movies made by Disney.
In math, the imaginary unit (written as "i" or "j") is a mathematical constant that only exists outside of the real numbers and is used in algebra. When we multiply the imaginary unit by a real number, we call the result an imaginary number. Though imaginary numbers can be used to solve a lot of mathematical problems, they cannot be represented by an amount of real life objects. History. Imaginary units were invented to answer the polynomial equation formula_1, which normally has no solution (see below). The term "imaginary" comes from by René Descartes and was meant to be insulting as, like zero and negative numbers at other times in history, imaginary numbers were thought to be useless as they are not natural. It wasn't until later centuries that the work of mathematicians like Leonhard Euler, Augustin-Louis Cauchy and Carl Friedrich Gauss would prove that imaginary numbers were very important for some areas of algebra. Definition. A common rule for multiplying and dividing numbers is that if the signs are different then the result is negative (e.g. formula_2), but if both numbers have the same sign then the result will be positive (e.g. formula_3 and formula_4). However, this leads to problems with square root numbers of negatives, as two negative numbers will always make a positive number: formula_5 so formula_6 but formula_7 as formula_8 To fill in this value gap the imaginary unit was made, which is defined as formula_9 and formula_10. Using imaginary numbers we can solve our last example: formula_11 formula_12 formula_6 and formula_14 Square root of i. Although the imaginary unit comes from solving a quadratic equation (an equation where the unknown appears squared), we could ask whether we need to create new number values like the imaginary unit to solve equations where higher powers of formula_15 like formula_16 and formula_17 appear. For example, the equation formula_18 has a fourth power of the unknown variable formula_15. Do we need new units like formula_20 to solve this equation? We could also ask a similar question: we needed to create a new number to find the square root of
Phycology (or algology), a part of botany, is the study of algae. Algae are important as primary producers in aquatic ecosystems. Most algae are eukaryotic, photosynthetic organisms that live in a wet environment. They are different from the higher plants by a lack of "normal" roots, stems or leaves. Many types have one cell and are very small or microscopic (including plankton and other microalgae); many others have many cells; some of these are very big, like seaweeds such as kelp and "Sargassum". Phycology includes the study of prokaryotic forms known as blue-green algae or cyanobacteria. Some microscopic algae are also in lichens. A phycologist is a person who studies phycology...
Snorkeling is swimming while using a tube to breathe underwater. Overview. Snorkeling is a very popular activity, particularly in places with clear, calm, warm oceans. It allows people to see underwater life in a natural setting, without the complicated equipment and training required for scuba diving.  Activity. Generally, people snorkel in shallow reefs ranging from sea level to 4 meters (13 feet) deep. Snorkelers can also explore deep water reefs. However, to see deeper reefs, a snorkeler has to hold their breath and dive down to the reef to see it. This kind of snorkeling takes more skill and fitness than shallow water snorkeling. It is also more dangerous than shallow water snorkeling. Snorkelers use masks so they can see underwater. This allows them to see fish, coral reefs and other forms of sea life. History. Man has always been interested by what is under the ocean. Evidence shows that people have been free diving for at least 5,000 years. The earliest known free divers were sponge farmers in Crete, who lived around 3000 B.C.E. These farmers used free diving to collect underwater sponges. They used hollow reeds like modern snorkels, to allow them to breathe while underwater. Equipment. Snorkelers use three basic pieces of equipment: Differences with scuba diving. Snorkeling is swimming on the surface of the water, with the head and nose under the water, using a diving mask, snorkel, and diving fins. Scuba diving is swimming with the whole body underwater. Scuba divers breathe through an oxygen tank, which allows them to breathe underwater for long periods at a time. Scuba divers also wear a tight diving suit, a diving mask, and diving fins. Before a person can scuba dive, they have to get training how to use the breathing equipment and dive to deep waters. Snorkeling does not require any training. People who cannot swim can still snorkel if they use a life jacket to keep them floating on the water.
Kelly Tarlton's Antarctic Encounter and Underwater World is an aquarium in Auckland, New Zealand. It is all underground and within the walls of Auckland City's sewage holding tanks, unused since 1961. It opened on January 25, 1985. Kelly Tarlton, an avid diver, treasure hunter and undersea explorer, was responsible for the Underwater World concept and construction.  Construction took 10 months and cost $3 million. Kelly Tarlton died suddenly of a heart attack on March 17, 1985, seven weeks after the Underwater World opened. Large sharks, stingrays and 1500 fish of forty different species may be viewed through a 114 metre-long underwater plexiglass tunnel in a figure-of-eight shape. The plexiglass is 7 centimetres thick.
Grave, shortened as "gv", was the word that was used to describe mass before the word "kilogram" was introduced. "Grave" comes from the word "gravity" and was first used in 1793 in France. The name "kilogram" was introduced in 1795 but was not the official word for mass until 1875. In order to have full consistency in the International System of Units (SI), many people think that the kilogram should be called something different. Using the word "kilogram" creates a problem because it is a base unit that has the prefix "kilo" already in its name. To fix the problem, some people have suggested using the word "grave" again.