AcharyaChanakya/simple-wikipedia huggingface dataset:
Australia Day and Anzac Day are both Australian holidays. A Barbecue is traditionally eaten on those days. Australia was colonised by people from Britain, but today people from all over the world live there. English is the main spoken language, and Christianity is the main religion, though all religions are accepted and not everybody has a religion. Australia is multicultural, which means that all its people are encouraged to keep their different languages, religions and ways of life, while also learning English and joining in with other Australians.
Famous Australian writers include the bush balladeers Banjo Paterson and Henry Lawson who wrote about life in the Australian bush. More modern famous writers include Peter Carey, Thomas Keneally and Colleen McCullough. In 1973, Patrick White won the Nobel Prize in Literature, the only Australian to have achieved this; he is seen as one of the great English-language writers of the twentieth century.
Australian music has had lots of world-wide stars, for example the opera singers Nellie Melba and Joan Sutherland, the rock and roll bands Bee Gees, AC/DC and INXS, the folk-rocker Paul Kelly (musician), the pop singer Kylie Minogue and Australian country music stars Slim Dusty and John Williamson. Australian Aboriginal music is very special and very ancient: it has the famous digeridoo woodwind instrument.
Australian TV has produced many successful programs for home and overseas - including Skippy the Bush Kangaroo, Home and Away and Neighbours - and produced such well known TV stars as Barry Humphries ("Dame Edna Everage"), Steve Irwin ("The Crocodile Hunter") and The Wiggles. Major Australian subgroups such as the Bogan have been shown on Australian TV in shows such as Bogan Hunters and Kath & Kim.
Australia has two public broadcasters (the ABC and the multi-cultural SBS), three commercial television networks, three pay-TV services, and numerous public, non-profit television and radio stations. Each major city has its daily newspapers, and there are two national daily newspapers, "The Australian" and "The Australian Financial Review".
Australian movies have a very long history. The world's first feature movie was the Australian movie "The Story of the Kelly Gang" of 1906. In 1933, "In the Wake of the Bounty", directed by Charles Chauvel, had Errol Flynn as the main actor. Flynn went on to a celebrated career in Hollywood. The first Australian Oscar was won by 1942's "Kokoda Front Line!", directed by Ken G. Hall. In the 1970s and 1980s lots of big Australian movies and movie stars became world famous with movies like "Picnic at Hanging Rock", "Gallipoli" (with Mel Gibson), "The Man From Snowy River" and "Crocodile Dundee". Russell Crowe, Cate Blanchett and Heath Ledger became global stars during the 1990s and "Australia" starring Nicole Kidman and Hugh Jackman made a lot of money in 2008.
Australia is also a popular destination for business conferences and research, with Sydney named as one of the top 20 meeting destinations in the world.
Sport is an important part of Australian culture because the climate is good for outdoor activities. 23.5% Australians over the age of 15 regularly take part in organised sporting activities. In international sports, Australia has very strong teams in cricket, hockey, netball, rugby league and rugby union, and performs well in cycling, rowing and swimming. Local popular sports include Australian Rules Football, horse racing, soccer and motor racing. Australia has participated in every summer Olympic Games since 1896, and every Commonwealth Games. Australia has hosted the 1956 and 2000 Summer Olympics, and has ranked in the top five medal-winners since 2000. Australia has also hosted the 1938, 1962, 1982 and 2006 Commonwealth Games and are to host the 2018 Commonwealth Games. Other major international events held regularly in Australia include the Australian Open, one of the four Grand Slam tennis tournaments, annual international cricket matches and the Formula One Australian Grand Prix. Corporate and government sponsorship of many sports and elite athletes is common in Australia. Televised sport is popular; some of the highest-rated television programs include the Summer Olympic Games and the grand finals of local and international football competitions.
The main sporting leagues for males are the Australian Football League, National Rugby League, A-League and NBL.
For women, they are ANZ Netball Championships, W-League and WNBL.
Famous Australian sports players include the cricketer Sir Donald Bradman, the swimmer Ian Thorpe and the athlete Cathy Freeman.
Just 60 years ago, Australia had only one big art festival. Now Australia has hundreds of smaller community-based festivals, and national and regional festivals that focus on specific art forms.
Australia is home to many animals that can be found nowhere else on Earth, which include: the koalas, the kangaroos, the wombat, the numbat, the emu, among many others. Most of the marsupials in the world are found only on the continent or on the neighbouring island of New Guinea. Wildfires from global warming in 2020 have decreased their population.
American English or United States English is the dialect of the English language spoken in the United States of America. It is different in some ways from other types of English, such as British English. Many types of American English came from local dialects in England.
Many people today know about American English even if they live in a country where another sort of English is spoken. This may be because people hear and read American English through the media, for example movies, television, and the Internet, where the most common form of English is American English.
Because people all over the world use the English language, it gets many new words. English has been changing in this way for hundreds of years. For example, the many millions who speak Indian English frequently add American English words to go along with its British English base and many other words from the various Indian languages.
Sometimes people learn American English as it is spoken in America. For example, in telephone call centers in India and other places, people often learn American English to sound more like their customers who call from America. These people often keep using American English in everyday life.
The meaning of many words are different in American English. Most changes in a language start with small things. For example, Italian, Spanish, and French all came from Latin.
There are many words that sound the same in both American English and British English, but are spelled differently. For example:
Books show that many of these differences come from the writings of English-lover Noah Webster, who made the American dictionary following the American War of Independence.
Some more differences in American English:
There are also some words in American English that are a bit different from British English, e.g.:
General American English is the kind most spoken in mass media. It more vigorously pronounces the letter "R" than some other kinds do. "R-dropping" is frequent in certain places where "r" sound is not pronounced after a vowel. For example as in the words "car" and "card" sounding like "cah" and "cahd". This occurs in the Boston area.
Aquaculture is the farming of fish, shrimp, abalones, algae, and other seafood. Aquaculture supplies fish, such as catfish, salmon, and trout. It was developed a few thousand years ago in China. Aquaculture supplies over 20% of all the seafood harvested.
Fish farming has been practiced, in some parts of the world, for thousands of years. Goldfish originated about a thousand years ago in carp farms in China, and the Roman Empire farmed oysters and other seafood. Today, half of the seafood eaten in the U.S. is farmed. To help meet the growing global demand for seafood, aquaculture is growing fast.
The environmental impact of fish farming varies widely, depending on the species being farmed, the methods used and where the farm is located. When good practices are used, it's possible to farm seafood in a way that has very little impact to the environment. Such operations limit habitat damage, disease, escapes of farmed fish and the use of wild fish as feed.
An abbreviation is a shorter way to write a word or phrase. People use abbreviations for words that they write a lot. The English language occasionally uses the apostrophe mark ' to show that a word is written in a shorter way, but some abbreviations do not use this mark. More often, they use periods, especially the ones that come from the Latin language. Common Latin abbreviations include i.e. [id est] "that is", e.g. [exempli gratia] "for example", and et al. [et alia] "and others".
Some new abbreviations have been created by scientists, by workers in companies and governments, and by people using the Internet.
People often think words are abbreviations when in fact they are acronyms.
Here are examples of common acronyms: The word "radar" is an acronym for "Radio Detection and Ranging". The name of the large computer company IBM comes from the words "International Business Machines". The name of the part of the United States government that sends rockets into outer space is NASA, from the words "National Aeronautics and Space Administration". When people using the Internet think that something is very funny, they sometimes write "LOL" to mean "Laughing Out Loud". People sometimes write "ASAP" for "As Soon As Possible".
In many mythologies and religions, an angel is a good spirit. The word angel comes from the Greek word "angelos" which means "messenger". Angels appear frequently in the Old Testament, the New Testament, Qur'an and Aqdas.
The study of Angels is called Angelology.
Angels are powerful, smart spirits that obey God's commands and praise him with singing and they have male (masculine)gender, but without any sex. They sometimes appear to humans in human form. They can deliver messages to people in person or in dreams. Angels that are named in the Bible are Michael (called a "chief prince"), Gabriel (known for telling Mary that she would be the mother of Jesus), and Raphael (in the Apocryphal Book of Tobit). The Ethiopian Book of Enoch also lists four Archangels which watch over the four quadrants of heaven; Michael, Raphael, Gabriel and Uriel. Lucifer is also known as an angel in the Bible.
Ezekiel 28:13-14
13. Thou hast been in Eden the garden of God; every precious stone was thy covering, the sardius, topaz, and the diamond, the beryl, the onyx, and the jasper, the sapphire, the emerald, and the carbuncle and gold: the workmanship of thy tabrets and of thy pipes was prepared in thee in the day that thou wast created.
14. Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.
It describes the sound of their wings, "like the roar of rushing waters."
Ezekiel 10:5-7 ; Ezekiel 10:8 reveals that they have hands like a man under their wings .
Ezekiel 1:7 KJV reveals that they look like man but are different because they have "straight feet" and four wings and four faces.
Ezekiel ch 1, and 10 describe the cherubim creatures ascending and descending from the earth with wheels. Ezekiel 1:14-20 ; Ezekiel 10:16
Ezekiel 10:9-13 describes what the wheels appeared to look like, and how they moved around, how they moved or flew through the sky quickly but turned not as they went; and how the inside workings of the wheels appeared to be "a wheel in the midst of a wheel" and that the color of the wheels was the color of "Amber" Stone. There are four separate wheels in both accounts, one for each single cherub which is there.
They are often shown in art as having wings and a halo. The wings represent their speed, and the halo represents their holiness.
The cherubim in art always appear as baby faced angels with very small non useful wings.
The cherubim statue or bronze casting of cherubim in the Temple of Solomon depicted them as two four winged creatures whose wings touched at the peak of the ark that they were making.
The same cherubim creatures were said to be cast in gold on top of the Ark of the Covenant. Casting metal is one of the oldest forms of artwork, and was attempted by Leonardo da Vinci.
Seeing repetitive numbers are thought to be associated with numerology, also referred to as angel numbers. It is believed that angels communicate with humans through repetitive appearances of numbers.
Ad hominem is a Latin word for a type of argument. It is a word often used in rhetoric. Rhetoric is the science of speaking well, and convincing other people of your ideas.
Translated to English, "ad hominem" means "against the person". In other words, when someone makes an ad hominem, they are attacking the person they are arguing against, instead of what they are saying.
The term comes from the Latin word "homo", which means human. "Hominem" is a gender neutral version of the word "homo". In ancient Rome it referred to all free men, or in other words, all free human beings.
Ad hominem can be a way to use reputation, rumors and hearsay to change the minds of other people listening. When a social network has already excluded or exiled one person, or applied a negative label to them, this can work more often.
It is most of the time considered to be a weak and poor argument. In courts and in diplomacy ad hominems are not appreciated.
Ad hominems are not wrong every time. For example, when people think that someone can't be trusted, things that they have said previously can be doubted.
In logic, a proof is something that starts with premises, and goes through a few logical arguments, to reach a conclusion.
In this example it can be seen that the (completely unrelated) fact that person A is uneducated and poor is used to prove that abortion should not be illegal.
Native Americans (also called Aboriginal Americans, American Indians, Amerindians or indigenous peoples of the Americas) are the people and their descendants, who were in the Americas when Europeans arrived.
Sometimes these people are called Indians, but this may be confusing, because it is the same word used for people from India. When Christopher Columbus explored, he did not know about the Americas. He was in the Caribbean but thought he was in the East Indies, so he called the people Indians.
There are many different tribes of Native American people, with many different languages. Some tribes were hunter-gatherers who moved from place to place. Others lived in one place and built cities and kingdoms.
Many Native Americans died after the Europeans came to the Americas. There were diseases that came with the Europeans but were new to the Native Americans. There were battles with the Europeans. Many native people were hurt, killed, or forced to leave their homes by settlers who took their lands.
Today, there are more than three million Native Americans in Canada and the U.S. combined. About 51 million more Native Americans live in Latin America. Many Native Americans still speak native languages and have their own cultural practices, while others have adopted some parts of Western culture. Many Native Americans face problems with discrimination and racism.
The ancestors of Native Americans came to the Americas from Asia. Some of them may have come to America 15,000 years ago when Alaska was connected to Siberia by the Bering land bridge.
The earliest people in the Americas came from Siberia when there was an ice bridge across the Bering Strait. The cold but mainly grassy plain which connected Siberia with Canada is called Beringia. It is reckoned that a few thousand people arrived in Beringia from eastern Siberia during the Last Glacial Maximum before moving into the Americas sometime after 16,500 years before the present (BP). This would have occurred as the American glaciers blocking the way southward melted, but before the bridge was covered by the sea about 11,000 years BP.
Before European colonization, Beringia was inhabited by the Yupik peoples on both sides of the straits. This culture remains in the region today, with others. In 2012, the governments of Russia and the United States announced a plan to formally establish "a transboundary area of shared Beringian heritage". Among other things this agreement would establish close ties between the Bering Land Bridge National Preserve and the Cape Krusenstern National Monument in the United States and Beringia National Park in Russia.
Native Americans are divided into many small nations, called First Nations in Canada and tribes elsewhere.
Each Native American tribe has their own culture. The cultures can be grouped together depending on region. For example, the tribes living in Mesoamerica have similar cultures.
Native Americans ate many different things depending on where they lived.
Native Americans from Mesoamerica introduced vanilla, avocados, and chocolate to the world.
Before Europeans came, the native peoples of the Americans practiced many different religions. Each tribe had their own different beliefs.
Today, many Native Americans practice Christianity, a religion that was brought to the Americas by Europeans. Meanwhile, others still practice their own religions.
Native Americans today speak over a thousand different languages. Some of these languages had writing systems before Europeans came.
Many of these languages are endangered because more people are speaking European languages and not teaching Native American languages to their kids.
Native Americans make musical instruments using the things around them.
Native Americans make a lot of different art.
According to the 2010 United States census, 0.9% of Americans say they are Native American, 2.9 million people, and 1.7% of Americans say they are both Native American and something else. They are not evenly spread out through the United States. About a third of the people in Alaska are Native Alaskan and about a sixth of the people in Oklahoma are Native American.
In the United States, most Native Americans live in cities. About 28% of Native Americans live on reservations. Many Native Americans are poor, and 24% are extremely poor. The history of violence against Native Americans persists today in higher rates of violence against Native American people than white people.
About 40% of the people of Guatemala identify as Native American. Many indigenous groups in the country are descendants of the Maya.
Many Native Americans in Guatemala are poor. Many of them have left the country to find better jobs elsewhere.
The majority of Bolivians belong to indigenous groups.
In the later half of the 20th century, many Native Americans started to protest the unfair treatment they experienced from the societies they lived in.
Some Native Americans have become famous in politics. For example, an Aymara man named Evo Morales was elected as president of Bolivia in 2005. He was the first indigenous presidential candidate in Bolivia and South America.
The apple tree (Malus domestica) is a tree that grows apples. It is best known for this juicy, tasty fruit. The tree is grown worldwide. Its fruit is low-cost, and is harvested all over the world.
Applewood is a type of wood that comes from this tree.
The apple tree comes from southern Kazakhstan, Kyrgyzstan, Tajikistan, and northwestern part of China. Apples have been grown for thousands of years in Asia and Europe. They were brought to North America by European settlers. Apples have religious and mythological significance in many cultures.
Apples are generally propagated by grafting, although wild apples grow readily from seed. Apple trees are large if grown from seed, but small if grafted onto roots (rootstock). There are more than 7,500 known cultivars of apples, with a range of desired characteristics. Different cultivars are bred for various tastes and uses: cooking, eating raw and cider production are the most common uses.
Trees and fruit are attacked by fungi, bacteria and pests. In 2010, the fruit's genome was sequenced as part of research on disease control and selective breeding in apple production.
Worldwide production of apples in 2013 was 90.8 million tonnes. China grew 49% of the total.
The apple has a small, leaf-shedding tree that grows up to tall. The apple tree has a broad crown with thick twigs.
The leaves are alternately arranged simple ovals. They are 5 to 12 centimetres long and 3–6centimetres (1.2–2.4in) wide. It has a sharp top with a soft underside. Blossoms come out in spring at the same time that the leaves begin to bud. The flowers are white. They also have a slightly pink color. They are five petaled, and 2.5 to 3.5 centimetres (0.98 to 1.4 in) in diameter. The fruit matures in autumn. It is usually 5 to 9 centimetres (2.0 to 3.5 in) in diameter. There are five carpels arranged in a star in the middle of the fruit. Every carpel has one to three seeds.
The wild ancestor of apple trees is "Malus sieversii". They grow wild in the mountains of Central Asia in the north of Kazakhstan, Kyrgyzstan, Tajikistan, and Xinjiang, China, and possibly also "Malus sylvestris". Unlike domesticated apples, their leaves become red in autumn. They are being used recently to develop "Malus domestica" to grow in colder climates.
The apple tree was possibly the earliest tree to be cultivated. Its fruits have become better over thousands of years. It is said that Alexander the Great discovered dwarf apples in Asia Minor in 300 BC. Asia and Europe have used winter apples as an important food for thousands of years. From when Europeans arrived, Argentina and the United States have used apples as food as well. Apples were brought to North America in the 1600s. The first apple orchard on the North American continent was said to be near Boston in 1625. In the 1900s, costly fruit industries, where the apple was a very important species, began developing.
In Norse mythology, the goddess Iðunn gives apples to the gods in "Prose Edda" (written in the 13th century by Snorri Sturluson) that makes them young forever. English scholar H. R. Ellis Davidson suggests that apples were related to religious practices in Germanic paganism. It was from there, she claims, that Norse paganism developed. She points out that buckets of apples were discovered in the place of burial for the Oseberg ship in Norway. She also remarks that fruit and nuts (Iðunn having been described as changing into a nut in "Skáldskaparmál") have been discovered in the early graves of the Germanic peoples in England. They have also been discovered somewhere else on the continent of Europe. She suggests that this may have had a symbolic meaning. Nuts are still a symbol of fertility in Southwest England.
Sometimes apples are eaten after they are cooked. Often apples are eaten uncooked. Apples can also be made into drinks. Apple juice and apple cider are apple drinks.
The flesh of the fruit is firm with a taste anywhere from sour to sweet. Apples used for cooking are sour, and need to be cooked with sugar, while other apples are sweet, and do not need cooking. There are some seeds at the core, that can be removed with a tool that removes the core, or by carefully using a knife.
The scientific name of the apple tree genus in the Latin language is "Malus". Most apples that people grow are of the "Malus domestica" species.
Most apples are good to eat raw (not cooked), and are also used in many kinds of baked foods, such as apple pie. Apples are cooked until they are soft to make apple sauce.
Apples are also made into the drinks apple juice and cider. Usually, cider contains a little alcohol, about as much as beer. The regions of Brittany in France and Cornwall in England are known for their apple ciders.
If one wants to grow a certain type of apple it is not possible to do this by planting a seed from the wanted type. The seed will have DNA from the apple that the seeds came from, but it will also have DNA from the apple flower that pollinated the seeds, which may well be a different type. This means that the tree which would grow from planting would be a mixture of two. In order to grow a certain type of apple, a small twig, or 'scion', is cut from the tree that grows the type of apple desired, and then added on to a specially grown stump called a rootstock. The tree that grows will only create apples of the type needed.
There are more than 7,500 known cultivars (varieties) of apples. Different cultivars are available for temperate and subtropical climates. One large collection of over 2,100 apple cultivars is at the National Fruit Collection in England. Most of these cultivars are grown for eating fresh (dessert apples). However, some are grown simply for cooking or making cider. Cider apples are usually too tart to eat immediately. However, they give cider a rich flavor that dessert apples cannot.
Most popular apple cultivars are soft but crisp. Colorful skin, easy shipping, disease resistance, 'Red Delicious' apple shape, and popular flavor are also needed. Modern apples are usually sweeter than older cultivars. This is because popular tastes in apples have become different. Most North Americans and Europeans enjoy sweet apples. Extremely sweet apples with hardly any acid taste are popular in Asia and India.
In the United Kingdom there are about 3000 different types of apples. The most common apple type grown in England is the 'Bramley seedling', which is a popular cooking apple.
Apple orchards are not as common as they were in the early 1900s, when apples were rarely brought in from other countries. Organizations such as Common Ground teach people about the importance of rare and local varieties of fruit.
Many apples are grown in temperate parts of the United States and Canada. In many areas where apple growing is important, people have huge celebrations:
There are many different varieties of apples, including:
Apples are in the group Maloideae. This is a subfamily of the family "Rosaceae". They are in the same subfamily as pears.
Abrahamic religion
An Abrahamic religion is a religion whose followers believe in the prophet Abraham. They believe Abraham and his sons/grandsons hold an important role in human spiritual development. The best known Abrahamic religions are Judaism, Christianity and Islam. Smaller religious traditions sometimes included as Abrahamic religions are Samaritanism, Druze, Rastafari, Yazidi, Babism and Bahá'í Faith. Mandaeism (a religion that holds many Abrahamic beliefs) is not called Abrahamic because its followers think Abraham was a false prophet
True Abrahamic religions are monotheistic (the belief that there is only one God). They also all believe that people should pray to God and worship God often. Among monotheistic religions, the Abrahamic religions have the world's largest number of followers. They are also all ethical monotheistic religions. This means they have rules that they have to follow.
Algebra (from Arabic: الجبر‎, transliterated "al-jabr", meaning "reunion of broken parts") is a part of mathematics (often called math in the United States and maths or numeracy in the United Kingdom ). It uses variables to represent a value that is not yet known. When an equals sign (=) is used, this is called an equation. A very simple equation using a variable is: 2 + 3 = x. In this example, x = 5, or it could also be said that "codice_1 equals five". This is called "solving for codice_1".
Besides equations, there are inequalities ("less than" and "greater than"). A special type of equation is called the function. This is often used in making graphs because it always turns one input into one output.
Algebra can be used to solve real problems because the rules of algebra work in real life and numbers can be used to represent the values of real things. Physics, engineering and computer programming are areas that use algebra all the time. It is also useful to know in surveying, construction and business, especially accounting.
People who do algebra use the rules of numbers and mathematic operations used on numbers. The simplest are adding, subtracting, multiplying, and dividing. More advanced operations involve exponents, starting with squares and square roots.
Algebra was first used to solve equations and inequalities. Two examples are linear equations (the equation of a straight line, y=mx+b or codice_3) and quadratic equations, which has variables that are squared (multiplied by itself, for example: 2*2, 3*3, or x*x).
Early forms of algebra were developed by the Babylonians and the Greek geometers such as Hero of Alexandria. However the word "algebra" is a Latin form of the Arabic word "Al-Jabr" ("casting") and comes from a mathematics book "Al-Maqala fi Hisab-al Jabr wa-al-Muqabilah", ("Essay on the Computation of Casting and Equation") written in the 9th century by a Persian mathematician, Muhammad ibn Mūsā al-Khwārizmī, who was a Muslim born in Khwarizm in Uzbekistan. He flourished under Al-Ma'moun in Baghdad, Iraq through 813-833 AD, and died around 840 AD. The book was brought into Europe and translated into Latin in the 12th century. The book was then given the name 'Algebra'. (The ending of the mathematician's name, al-Khwarizmi, was changed into a word easier to say in Latin, and became the English word "algorithm").
Here is a simple example of an algebra problem:
These are the steps you can use to solve the problem:
With practice, algebra can be used when faced with a problem that is too hard to solve any other way. Problems such as building a freeway, designing a cell phone, or finding the cure for a disease all require algebra.
As in most parts of mathematics, adding "z" to "y" (or "y" plus "z") is written as "y" + "z".
Subtracting "z" from "y" (or "y" minus "z") is written as "y" − "z".
Dividing "y" by "z" (or "y" over "z": formula_1) is written as "y" ÷ "z" or y/z. "y"/"z" is more commonly used.
In algebra, multiplying "y" by "z" (or "y" times "z") can be written in 4 ways: "y × z", "y * z", "y·z", or just "yz". The multiplication symbol "×" is usually not used, because it looks too much like the letter x, which is often used as a variable. Also, when multiplying a larger expression, parentheses can be used: "y" ("z+1").
When we multiply a number and a letter in algebra, we write the number in front of the letter: 5 × "y" = 5"y". When the number is 1, then the 1 is not written because 1 times any number is that number (1 × "y" = "y") and so it is not needed.
As a side note, you do not have to use the letters "x" or "y" in algebra. Variables are just symbols that mean some unknown number or value, so you can use any variable. "x" and "y" are the most common, though.
An important part of algebra is the study of functions, since functions often appear in equations that we are trying to solve. A function is like a machine you can put a number (or numbers) into and get a certain number (or numbers) out. When using functions, graphs can be powerful tools in helping us to study the solutions to equations.
A graph is a picture that shows all the values of the variables that make the equation or inequality true. Usually this is easy to make when there are only one or two variables. The graph is often a line, and if the line does not bend or go straight up-and-down it can be described by the basic formula y = mx + b. The variable "b" is the y-intercept of the graph (where the line crosses the vertical axis) and "m" is the slope or steepness of the line. This formula applies to the coordinates of a graph, where each point on the line is written (x, y).
In some math problems like the equation for a line, there can be more than one variable ("x" and "y" in this case). To find points on the line, one variable is changed. The variable that is changed is called the "independent" variable. Then the math is done to make a number. The number that is made is called the "dependent" variable. Most of the time the independent variable is written as "x" and the dependent variable is written as "y", for example, in y = 3x + 1. This is often put on a graph, using an "x" axis (going left and right) and a "y" axis (going up and down). It can also be written in function form: f(x) = 3x + 1. So in this example, we could put in 5 for "x" and get y = 16. Put in 2 for "x" would get y=7. And 0 for "x" would get y=1. So there would be a line going thru the points (5,16), (2,7), and (0,1) as seen in the graph to the right.
If x has a power of 1, it is a straight line. If it is squared or some other power, it will be curved. If it uses an inequality ("<" or ">"), then usually part of the graph is shaded, either above or below the line.
In algebra, there are a few rules that can be used for further understanding of equations. These are called the rules of algebra. While these rules may seem senseless or obvious, it is wise to understand that these properties do not hold throughout all branches of mathematics. Therefore, it will be useful to know how these axiomatic rules are declared, before taking them for granted. Before going on to the rules, reflect on two definitions that will be given.
'Commutative' means that a function has the same result if the numbers are swapped around. In other words, the order of the terms in an equation do not matter. When the operator of two terms is an addition, the 'commutative property of addition' is applicable. In algebraic terms, this gives formula_6.
Note that this does not apply for subtraction! (i.e. formula_7)
When the operator of two terms is an multiplication, the 'commutative property of multiplication' is applicable. In algebraic terms, this gives formula_8.
Note that this does not apply for division! (i.e. formula_9, when formula_10)
'Associative' refers to the grouping of numbers. The associative property of addition implies that, when adding three or more terms, it doesn't matter how these terms are grouped. Algebraically, this gives formula_11. Note that this does not hold for subtraction, e.g. formula_12 (see the distributive property).
The associative property of multiplication implies that, when multiplying three or more terms, it doesn't matter how these terms are grouped. Algebraically, this gives formula_13. Note that this does not hold for division, e.g. formula_14.
The distributive property states that the multiplication of a number by another term can be distributed. For instance: formula_15. (Do "not "confuse this with the associative properties! For instance, formula_16.)
'Identity' refers to the property of a number that it is equal to itself. In other words, there exists an operation of two numbers so that it equals the variable of the sum. The additive identity property states that the sum of any number and 0 is that number: formula_17. This also holds for subtraction: formula_18.
The multiplicative identity property states that the product of any number and 1 is that number: formula_19. This also holds for division: formula_20.
The additive inverse property is somewhat like the opposite of the additive identity property. When an operation is the sum of a number and its opposite, and it equals 0, that operation is a valid algebraic operation. Algebraically, it states the following: formula_21. Additive inverse of 1 is (-1).
The multiplicative inverse property entails that when an operation is the product of a number and its reciprocal, and it equals 1, that operation is a valid algebraic operation. Algebraically, it states the following: formula_22. Multiplicative inverse of 2 is 1/2.
In addition to "elementary algebra", or basic algebra, there are advanced forms of algebra, taught in colleges and universities, such as abstract algebra, linear algebra, and universal algebra.
This includes how to use a matrix to solve many linear equations at once. "Abstract algebra" is the study of things that are found in equations, going beyond numbers to the more abstract with groups of numbers.
Many math problems are about physics and engineering. In many of these physics problems time is a variable. Time uses the letter "t". Using the basic ideas in algebra can help reduce a math problem to its simplest form making it easier to solve difficult problems. Energy is "e", force is "f", mass is "m", acceleration is "a" and speed of light is sometimes "c". This is used in some famous equations, like f = ma and e=mc^2 (although more complex math beyond algebra was needed to come up with that last equation).
Atoms are very small pieces of matter. There are many different types of atoms, each with its own name, mass and size. These different types of atoms are called chemical elements. The chemical elements are organized on the periodic table. Examples of elements are hydrogen and gold.
Atoms are very small, but their exact size depends on the element. Atoms range from 0.1 to 0.5 nanometers in width. One nanometer is about 100,000 times smaller than the width of a human hair. This makes atoms impossible to see without special tools. Scientists discover how they work and interact with other atoms through experiments.
Atoms can join together to make molecules: for example, two hydrogen atoms and one oxygen atom combine to make a water molecule. When atoms join together it is called a chemical reaction.
Atoms are made up of three kinds of smaller particles, called protons, neutrons and electrons. The protons and neutrons are heavier, and stay in the middle of the atom, which is called the nucleus. The nucleus is surrounded by a cloud of light-weight electrons, these are attracted to the protons in the nucleus by the electromagnetic force because they have opposite electric charges.
The number of protons an atom has defines what chemical element it is, this number is sometimes called its atomic number. For example, hydrogen has one proton and sulfur has 16 protons. Because the mass of neutrons and protons is very similar, and the mass of electrons is very small, we can call the amount of protons and neutrons in an atom its atomic mass.
Atoms move faster when they are in their gas form (because they are free to move) than they do in liquid form and solid matter. In solid materials, the atoms are tightly packed next to each other so they vibrate, but are not able to move (there is no room) as atoms in liquids do.
The word "atom" comes from the Greek (ἀτόμος) "atomos", "indivisible", from (ἀ)-, "not," and τόμος, "a cut." The first historical mention of the word atom came from works by the Greek philosopher Democritus, around 400 BC. Atomic theory stayed as a mostly philosophical subject, with not much actual scientific investigation or study, until the development of chemistry in the 1650s.
In 1777 French chemist Antoine Lavoisier defined the term "element" for the first time. He said that an element was any basic substance that could not be broken down into other substances by the methods of chemistry. Any substance that could be broken down was a "compound".
In 1803, English philosopher John Dalton suggested that elements were tiny, solid balls made of atoms. Dalton believed that all atoms of the same element have the same mass. He said that compounds are formed when atoms of more than one element combine. According to Dalton, in a certain compound, the atoms of the compound's elements always combine the same way.
In 1827, British scientist Robert Brown looked at pollen grains in water under his microscope. The pollen grains appeared to be jiggling. Brown used Dalton's atomic theory to describe patterns in the way they moved. This was called "brownian motion". In 1905 Albert Einstein used mathematics to prove that the seemingly random movements were caused by the reactions of atoms, and by doing this he conclusively proved the existence of the atom.
In 1869, Russian scientist Dmitri Mendeleev published the first version of the periodic table. The periodic table groups elements by their atomic number (how many protons they have. This is usually the same as the number of electrons).
Elements in the same column, or period, usually have similar properties. For example, helium, neon, argon, krypton and xenon are all in the same column and have very similar properties. All these elements are gases that have no colour and no smell. Also, they are unable to combine with other atoms to form compounds. Together they are known as the noble gases.
The physicist J.J. Thomson was the first person to discover electrons. This happened while he was working with cathode rays in 1897. He realized they had a negative charge, unlike protons (positive) and neutrons (no charge). Thomson created the plum pudding model, which stated that an atom was like plum pudding: the dried fruit (electrons) were stuck in a mass of pudding (protons). In 1909, a scientist named Ernest Rutherford used the Geiger–Marsden experiment to prove that most of an atom is in a very small space called the atomic nucleus. Rutherford took a photo plate and covered it with gold foil, and then shot alpha particles (made of two protons and two neutrons stuck together) at it. Many of the particles went through the gold foil, which proved that atoms are mostly empty space. Electrons are so small they make up only 1% of an atom's mass.
In 1913, Niels Bohr introduced the Bohr model. This model showed that electrons travel around the nucleus in fixed circular orbits. This was more accurate than the Rutherford model. However, it was still not completely right. Improvements to the Bohr model have been made since it was first introduced.
In 1925, chemist Frederick Soddy found that some elements in the periodic table had more than one kind of atom.
For example, any atom with 2 protons should be a helium atom. Usually, a helium nucleus also contains two neutrons. However, some helium atoms have only one neutron. This means they truly are helium, because an element is defined by the number of protons, but they are not normal helium, either. Soddy called an atom like this, with a different number of neutrons, an "isotope". To get the name of the isotope we look at how many protons and neutrons it has in its nucleus and add this to the name of the element. So a helium atom with two protons and one neutron is called helium-3, and a carbon atom with six protons and six neutrons is called carbon-12. However, when he developed his theory Soddy could not be certain neutrons actually existed. To prove they were real, physicist James Chadwick and a team of others created the mass spectrometer. The mass spectrometer actually measures the mass and weight of individual atoms. By doing this Chadwick proved that to account for all the weight of the atom, neutrons must exist.
In 1937, German chemist Otto Hahn became the first person to create nuclear fission in a laboratory. He discovered this by chance when he was shooting neutrons at a uranium atom, hoping to create a new isotope. However, he noticed that instead of a new isotope the uranium simply changed into a barium atom, a smaller atom than uranium. Apparently, Hahn had "broken" the uranium atom. This was the world's first recorded nuclear fission reaction. This discovery eventually led to the creation of the atomic bomb.
Further into the 20th century, physicists went deeper into the mysteries of the atom. Using particle accelerators they discovered that protons and neutrons were actually made of other particles, called quarks.
The most accurate model so far comes from the Schrödinger equation. Schrödinger realized that the electrons exist in a cloud around the nucleus, called the electron cloud. In the electron cloud, it is impossible to know exactly where electrons are. The Schrödinger equation is used to find out where an electron is likely to be. This area is called the electron's orbital.
The complex atom is made up of three main particles; the proton, the neutron and the electron. The isotope of Hydrogen Hydrogen-1 has no neutrons, just the one proton and one electron. Protons have a positive electric charge and electrons have a negative charge. A positive hydrogen ion has no electrons, just the one proton. These two examples are the only known exceptions to the rule that all other atoms have at least one proton, one neutron and one electron each.
Electrons are by far the smallest of the three atomic particles, their mass and size is too small to be measured using current technology. They have a negative charge. Protons and neutrons are of similar size and weight to each other, protons are positively charged and neutrons have no charge.
Most atoms have a neutral charge; because the number of protons (positive) and electrons (negative) are the same, the charges balance out to zero. However, in ions (different number of electrons) this is not always the case, and they can have a positive or a negative charge. Protons and neutrons are made out of quarks, of two types; up quarks and down quarks. A proton is made of two up quarks and one down quark and a neutron is made of two down quarks and one up quark.
The nucleus is in the middle of an atom. It is made up of protons and neutrons. Usually in nature, two things with the same charge repel or shoot away from each other. So for a long time it was a mystery to scientists how the positively charged protons in the nucleus stayed together. They solved this by finding a particle called a "gluon". Its name comes from the word "glue" as gluons act like atomic glue, sticking the protons together using the "strong nuclear force". It is this force which also holds the quarks together that make up the protons and neutrons.
The number of neutrons in relation to protons defines whether the nucleus is stable or goes through radioactive decay. When there are too many neutrons or protons, the atom tries to make the numbers the same by getting rid of the extra particles. It does this by emitting radiation in the form of alpha, beta or gamma decay. Nuclei can change through other means too. Nuclear fission is when the nucleus splits into two smaller nuclei, releasing a lot of stored energy. This release of energy is what makes nuclear fission useful for making bombs and electricity, in the form of nuclear power.
The other way nuclei can change is through nuclear fusion, when two nuclei join together, or fuse, to make a heavier nucleus. This process requires extreme amounts of energy in order to overcome the electrostatic repulsion between the protons, as they have the same charge. Such high energies are most common in stars like our Sun, which fuses hydrogen for fuel.
Electrons orbit, or travel around, the nucleus. They are called the atom's "electron cloud". They are attracted towards the nucleus because of the electromagnetic force. Electrons have a negative charge and the nucleus always has a positive charge, so they attract each other.
Around the nucleus, some electrons are further out than others, in different layers. These are called "electron shells". In most atoms the first shell has two electrons, and all after that have eight. Exceptions are rare, but they do happen and are difficult to predict. The further away the electron is from the nucleus, the weaker the pull of the nucleus on it. This is why bigger atoms, with more electrons, react more easily with other atoms.
The electromagnetism of the nucleus is not strong enough to hold onto their electrons and atoms lose electrons to the strong attraction of smaller atoms.
Some elements, and many isotopes, have what is called an "unstable nucleus". This means the nucleus is either too big to hold itself together or has too many protons or neutrons. When this happens the nucleus has to get rid of the excess mass or particles. It does this through radiation. An atom that does this can be called "radioactive". Unstable atoms continue to be radioactive until they lose enough mass/particles that they become stable. All atoms above atomic number 82 (82 protons, lead) are radioactive.
There are three main types of radioactive decay; alpha, beta and gamma.
Every radioactive element or isotope has what is named a "half-life". This is how long it takes half of any sample of atoms of that type to decay until they become a different stable isotope or element. Large atoms, or isotopes with a big difference between the number of protons and neutrons will therefore have a long half life, because they must lose more neutrons to become stable.
Marie Curie discovered the first form of radiation. She found the element and named it radium. She was also the first female recipient of the Nobel Prize.
Frederick Soddy conducted an experiment to observe what happens as radium decays. He placed a sample in a light bulb and waited for it to decay. Suddenly, helium (containing 2 protons and 2 neutrons) appeared in the bulb, and from this experiment he discovered this type of radiation has a positive charge.