Aarushhh/wikipedia-simple-splitted huggingface dataset:
Witchcraft and accusations of witchcraft are still very common in some parts of West Africa.

Witch crimes in the Malleus Maleficarum 
Control of procreation was a constant theme, as was medical knowledge:
Concerning Witches who copulate with Devils. Why is it that Women are chiefly addicted to Evil superstitions?
 Whether Witches may work some Prestidigatory Illusion so that the Male Organ appears to be entirely removed and separate from the Body.
 That Witches who are Midwives in Various Ways Kill the Child Conceived in the Womb, and Procure an Abortion; or if they do not this Offer New-born Children to Devils.
 How Witches Impede and Prevent the Power of Procreation.
 How, as it were, they Deprive Man of his Virile Member.
 Of the Manner whereby they Change Men into the Shapes of Beasts.
 Of the Method by which Devils through the Operations of Witches sometimes actually possess men.
 Of the Method by which they can Inflict Every Sort of Infirmity, generally Ills of the Graver Kind.
 Of the Way how in Particular they Afflict Men with Other Like Infirmities.
 How Witch Midwives commit most Horrid Crimes when they either Kill Children or Offer them to Devils in most Accursed Wise.
Witches in films and stories 

 Hocus Pocus, a film which is about three witches
 The Wizard Of Oz, a book/film which has a witch as the main villain
Famous people accused of witchcraft
 1431: Joan of Arc. She was burned at the stake on 30 May.
 1591: Elizabeth of Doberschütz. She was beheaded and burnt outside the gates of Stettin, on 17 December.
 1594: Maria Holl (also known as The Witch of Nördlingen). She was one of the first women to withstand being tortured during her witch trial of 1593-1594. She was eventually cleared of the accusations, which led some people to doubt the righteousness of witch trials. Through her force, Holl rid the town of Nördlingen of their witch craze. She died in 1634, probably from the plague.
 1612: The Samlesbury witches. In August 1612, they were found not guilty in one of the most famous witch trials in English history. However, ten other people were found guilty and were hanged.
 1635: Hester Jonas (also called The Witch of Neuss). She was beheaded and burnt on Christmas Eve in 1635, at about 64 years old. The complete proceedings of the trial are still available in Neuss.
1663: Anna Roleffes (better known as Tempel Anneke). She was one of the last witches to be executed in Braunschweig. She was beheaded on 30 December.
 1680: Catherine Monvoisin, a lover of Louis XIV who was close to Marquise the Montespan. She delivered poisons and held black masses for payment. In 1680, she was burnt to death along with some other accused witches on the Place de la Grève in Paris.
 1692: The witches accused during the Salem Witch Trials in Salem, Massachusetts. Today, Salem is called “the Witch City,” and historical sites related to the witch trials are tourist attractions.
 1751: Anna Schnidenwind. She was one of the last women to be publicly executed for witchcraft in Germany. On 24 April, in Endingen am Kaiserstuhl, she was strangled to death, then burned.
 1782: Anna Göldi (or Göldin). She was the last witch to be executed in Europe. Her execution happened in Glarus, Switzerland, in the summer of 1782.
References

Other websites

 Some historical notes on the witch-craze from the historian Trevor Roper 
 Kabbalah On Witchcraft - A Jewish view (Audio) chabad.org
 Jewish Encyclopedia: Witchcraft
 Witchcraft in the Catholic Encyclopedia on (New Advent)
 Witchcraft and Devil Lore in the Channel Islands, 1886, by John Linwood Pitts, from Project Gutenberg
 A Treatise of Witchcraft, 1616, by Alexander Roberts, from Project Gutenberg
 The Witches' Voice 1997-2007 The Witches' Voice Inc
Events and trends 
 1210
 Emperor Tsuchimikado ends his reign as Emperor of Japan
 Emperor Juntoku begins to rule Japan
 1212 Battle of Navas de Tolosa.
 1214 July – Battle of Bouvines; Philip II of France defeats Otto IV of Germany
 1215
 Fourth Council of the Lateran
 Otto IV deposed as King of Germany, replaced by Frederick II
 Magna Carta adopted
 Beijing captured by Mongols; the Yuan Dynasty in China begins this way.
The West Bank is a piece of land in the Middle East. It touches the Dead Sea and the River Jordan. The landscape is mostly hills or desert. The weather in the summer is hot and dry. It is cooler and rainy in the winter.
Right now, the area is under the control of Israel. Some Israelis and other nations disagree on whose it really is.
Since 1990 there are talks between the Israeli government and the Palestinians about what will happen in the West Bank and the Gaza Strip in the future. Most people on the West Bank are Palestinians but there are also many Jewish settlers in settlements. There has been some controversy about these settlements.

The State of Palestine claims the West Bank with East Jerusalem included.

The West Bank is divided into 165 Palestinian enclaves that are under partial Palestinian rule. The rest of the West Bank, including 200 Israeli settlements, is under full Israeli control.
Israeli settlers and civilians living or traveling through the West Bank are subject to Israeli law, and are represented in the Knesset; On the other hand, Palestinian civilians (and mostly stuck in or confined to scattered enclaves), are subject to martial law and are not permitted to vote in Israel's national elections.

Names
The West Bank is called Judea and Samaria Area by the Israeli government and some Jews and Christians.

Related pages 
 Human rights in West Bank
 LGBT rights in West Bank
 Israeli occupation of the West Bank

Other websites

IMEMC
Jerusalem Post

Sources
Jan Hus, or John Huss (c.1370 - 6 July 1415) was born in Husinec, Bohemia (now Czech Republic). He was a Bohemian religious thinker and reformer who started a religious movement that was strongly influenced by the beliefs of the English scholar John Wycliffe.

Hus studied at the University of Prague. Around 1400, he became a Catholic priest and soon accepted a position of preaching in Czech, the language that is spoken in Bohemia. While preaching, he studied Wycliffe’s writings and came to agree with them, especially because of how real they were.

In 1403, Hus asked the church to undo the ban on Wycliffe's writings, and hé translated them into Czech. The church, led by Rchbishop Zbynek Zajíc, refused. In 1410, Zajíc ordered for Hus's writings be burned and foe Hus and his followers, the Hussites, to be forced out of the church. Hus was excommunicated in 1411, condemned by the Council of Constance, and burned at the stake on 6 July 1415 in Konstanz, Germany.
When Hus was killed, his followers revolted and fought against the Catholics but were defeated in 1431.

Hus' teachings 
The (Catholic) Church is made of all those meant to be saved (ecclesia est universitas praedestinatorum). It is not made of the hierarchy of priests.
Christ is the head of the Church, not the Pope. It is therefore not necessary to obey the pope to be saved.

Many of his teachings were later taken up by Martin Luther.

References 

1369 births
1415 deaths
Christian ministers
Christianity of the Middle Ages
Czech people
Konstanz
People excommunicated by the Catholic Church
People executed by burning
Roman Catholics
Konstanz (English often Constance) is a university town with a population of around 80,000. It is on the shore of Lake Constance, in the south-west corner of Germany, near Switzerland.

The history of the city goes back to Ancient Rome. In the 15th century, the Council of Constance was held there and ended the Western Schism. Jan Hus was burned as a heretic at the council.

References

Other websites

 
Konstanz (district)
Panther can mean

 A black panther or white panther, which is a name for a leopard or jaguar with black or white fur.

 Any animal which belongs to the genus Panthera (e.g. lion) or the subfamily Pantherinae.

 In different regions different felines are also called panther: the leopard in Asia and Africa, the jaguar in South America, and the puma in North America (especially the ones that live in Florida, USA).

All these animals belong to the Felidae family.

National symbols of Gabon
Instant messaging (often shortened to IM) is a way of two or more people to communicate over a network. When the sender sends a message, this message is sent to all the recipients in the group.  People use messaging clients to send and receive messages. The type of message supported depends on the specific client, and network. Most of the time, it is text. In some cases, images or other types of media is supported.
Instant messaging services got many ideas from an older and still popular way to online chat named Internet Relay Chat (IRC). In early instant messaging programs, each letter appeared when it was typed and when letters were deleted to correct typos. These were also seen by the reader. This made it more like a telephone conversation than sending letters. In newer instant messaging programs, the other readers in the conversation generally only sees each line of text right after a new line is started. Most instant messaging programs have a way to set a status message. This works likes the message on a telephone answering machine. It shows whether or not people are online and want to chat.

Benefits
Benefits 

Instant messaging offers real-time communication and allows easy collaboration, which might be considered more akin to genuine conversation than email's "letter" format. In contrast to e-mail, the parties know whether the peer is available. Most systems allow the user to set an online status or away message so peers are notified when the user is available, busy, or away from the computer. On the other hand, people are not forced to reply immediately to incoming messages. For this reason, some people consider communication via instant messaging to be less intrusive than communication via phone. However, not all popular systems allow the sending of messages to people not currently logged on (offline messages), thus removing much of the difference between IM and email.
Instant messaging allows instantaneous communication between a number of parties simultaneously, by transmitting information quickly and efficiently, featuring immediate receipt of acknowledgment or reply. In certain cases IM involves additional features, which make it even more popular, i.e. to see the other party, e.g. by using ((web-cams)), or to talk directly for free over the internet.

It is possible to save a conversation to read later or look at again. Instant messages typically are may be logged in a local message history which closes the gap to the persistent nature of e-mails and facilitates quick exchange of information like URLs or document snippets (which can be unwieldy when communicated via telephone).

People with an auditory or speech disability
Instant messaging opens new methods of spontaneous communication for people that have an impairment in hearing, auditory processing, or speech.  It is considered by many a powerful way to allow equal opportunities in communication, without the aid of special devices or services designed for users with hearing loss.

Friend-to-friend networks 

Instant Messaging may be done in a Friend-to-friend network, in which each node connects to the friends on the friendslist. This allows to communicate to friends of friends and build chatrooms for instant messages with all friends on that network.

Business application
The adoption of IM across corporate networks outside of the control of IT organizations creates many risks and liabilities for companies who do not effectively manage and support IM use.  Companies implement specialized IM archiving and security products and services like those from Secure Computing, Akonix, Surfcontrol, and ScanSafe to mitigate these risks and provide safe, secure, productive instant messaging capabilities to their employees.

Risks 

Although instant messaging has many good things, it also has risks and liabilities, especially when used in workplaces. Among these are:

 Security risks (e.g. IM used to infect computers with spyware, viruses, trojans, worms)
 Compliance risks
 Inappropriate use
 Intellectual property leakage
In addition to the malicious code threat, the use of instant messaging at work also creates a risk of non-compliance to laws and regulations governing the use of electronic communications in businesses. In the United States alone there are over 10,000 laws and regulations related to electronic messaging and records retention. The more well-known of these include the Sarbanes-Oxley Act, HIPAA, and SEC 17a-3. Recent changes to Federal Rules of Civil Procedure, effective December 1, 2006, create a new category for electronic records which may be requested during discovery (law) in legal proceedings. Most countries around the world also regulate the use of electronic messaging and electronic records retention in similar fashion to the United States. The most common regulations related to IM at work involve the need to produce archived business communications to satisfy government or judicial requests under law
. Many instant messaging communications fall into the category of business communications that must be archived and retrievable.
Organizations of all types must protect themselves from the liability of their employees' inappropriate use of IM. The informal, immediate, and ostensibly anonymous nature of instant messaging makes it a candidate for abuse in the workplace. The topic of inappropriate IM use became front-page news in October 2006 when Congressman Mark Foley resigned his seat after admitting sending offensive instant messages of a sexual nature to underage former House pages from his Congressional office PC. The Mark Foley Scandal led to media coverage and mainstream newspaper articles warning of the risks of inappropriate IM use in workplaces. In most countries, corporations have a legal responsibility to ensure harassment-free work environment for employees. The use of corporate-owned computers, networks, and software to harass an individual or spread inappropriate jokes or language creates a liability for not only the offender but also the employer. A survey by IM archiving and security provider Akonix Systems, Inc
. in March 2007 showed that 31% of respondents had been harassed over IM at work. Companies now include instant messaging as an integral component of their policies on appropriate use of the World Wide Web, email, and other corporate assets.
Security and archiving 

In the early 2000s, a new class of IT security provider emerged to provide remedies for the risks and liabilities faced by corporations who chose to use IM for business communications. The IM security providers created new products to be installed in corporate networks for the purpose of archiving, content-scanning, and security-scanning IM traffic moving in and out of the corporation. Similar to the e-mail filtering vendors, the IM security providers focus on the risks and liabilities described above.

With rapid adoption of IM in the workplace, demand for IM security products began to grow in the mid-2000s. By 2007, the preferred platform for the purchase of security software had become the "appliance", according to IDC, who estimate that by 2008, 80% of network security products will be delivered via an appliance.

Related pages
 e-mail
 IRC

References

Other websites
Other websites 

Instant Messenger Security - Best Practices
All About Instant Messengers 
List of popular Mobile IM Clients 
Web Messengers Handbook

Instant messaging software
Messaging
AOL Inc. (previously America Online) is a U.S.-based online service provider and Internet service provider. It has been in business since 1985. Important services in the early years were online chat and online games. Most connections were dial-up. In 2001 AOL bought Time Warner. In 2009 after a spin-off from Time Warner they changed their name to AOL Inc. It was announced in May 2015 that Verizon Communications purchased AOL.

AOL Instant Messenger was a service which allowed users to communicate with any user currently online. AIM had millions of users worldwide. There were also other computer programs that could be used to talk with your AIM account, for example Trillian, Pidgin, Digsby, and AIM+. AIM was shut down on December 15, 2017.

Other AOL products are AOL Spyware Protection, AOL Safety and Security Center, ICQ, AOl Computer Check-Up, AOL Explorer, AOL TopSpeed, AOL Dialer, AOL One-Click Fixes and AOL Openride.

References

Other websites
 AOL US and headquarters
 AOL in other countries
American internet service providers
1985 establishments in the United States
A mailman or mail carrier or postman is a person who brings people their postal mail. Normally he works for the post office of the respective country. Of course, there are also women doing this job. They are called mailwomen. For a layman, this occupation is called "letter carriers". 

Fictional mailmen are traditionally shown as acting afraid of dogs, even to the point of shock.

Related pages 

 Despatch rider
 Persian couriers

Occupations
Postal officials
The Chinese postman problem is a mathematical problem of graph theory. It is also known as route inspection problem. Suppose there is a mailman who needs to deliver mail to a certain neighbourhood. The mailman is unwilling to walk far, so he wants to find the shortest route through the neighbourhood, that meets the following criteria:

 It is a closed circuit (it ends at the same point it starts).
 He needs to go through every street at least once.

If the graph travelled has an Eulerian path, this circuit is the ideal solution.

Alan Goldman of the U.S. National Bureau of Standards first coined the name 'Chinese Postman Problem' for this problem, as it was originally studied by the Chinese mathematician Mei-Ku Kuan in 1962.

Other websites 
Chinese postman problem (at MathWorld)

References

Graph theory
The four color theorem is a theorem of mathematics. It says that in any plane surface with regions in it (people think of them as maps), the regions can be colored with no more than four colors. Two regions that have a common border must not get the same color. They are called adjacent (next to each other) if they share a segment of the border, not just a point.

This was the first theorem to be proved by a computer, in a proof by exhaustion. In proof by exhaustion, the conclusion is established by dividing it into cases, and proving each one separately. There may be a lot of cases. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof was controversial because most of the cases were checked by a computer program, not by hand. The shortest known proof of the four color theorem today still has over 600 cases.
Even though the problem was first presented as a problem to color political maps of countries, mapmakers are not very interested in it. According to an article by the math historian Kenneth May , “Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of map making do not mention the four-color property.”

Many simpler maps can be colored using three colors. The fourth color is needed for some maps, such as one in which one region is surrounded by an odd number of others, which touch each other in a cycle. One such example is given in the image. The five color theorem states that five colors are enough to color a map. It has a short, elementary proof and was proven in the late 19th century.  Proving that four colors are all that is needed turned out to be much more difficult. Many false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.
Exact formulation of the problem
Intuitively, the four color theorem can be stated as 'given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two regions which are adjacent have the same color'. To be able to correctly solve the problem, it is necessary to clarify some aspects: First, all points that belong to three or more countries must be ignored. Secondly, bizarre maps with regions of finite area and infinite perimeter can require more than four colors.
For the purpose of the theorem every "country" has to be a simply connected region, or contiguous.
In the real world, this is not true: Alaska as part of the United States, Nakhchivan as part of Azerbaijan, and Kaliningrad as part of Russia are not contiguous. Because the territory of a particular country must be the same color, four colors may not be enough. For instance, consider a simplified map, such as the one shown on the left: In this map, the two regions labeled A belong to the same country, and must be the same color. This map then requires five colors, since the two A regions together are contiguous with four other regions, each of which is contiguous with all the others. If A had only three regions, six or more colors might be needed. In this way, it is possible to make maps that need an arbitrarily high number of colors. A similar construction also applies if a single color is used for all bodies of water, as is usual on real maps.
History
The first person to name the problem was Francis Guthrie, in 1852. He was a law student in England, at the time. He found that he needed at least four colors to color a map of the counties of England. Augustus de Morgan first discussed the problem, in a letter he wrote to Rowan Hamliton in August 1852. In the letter, de Morgan asks whether four colors are really enough to color a map, such that countries that are next to each other get different colors.
English mathematician Arthur Cayley presented the problem to the mathematical society in London, in 1878. Within a year, Alfred Kempe found what looked like a proof  of the problem. Eleven years later, in 1890, Percy Heawood showed that Alfred's proof was wrong. Peter Guthrie Tait presented another attempt at a proof in 1880. It took eleven years to show that Tait's proof did not work either. In 1891, Julius Petersen could show this. When he falsified Cayley's proof, Kempe also showed a proof for a problem he called Five color theorem. The theorem says that any such map can be colored with no more than five colors. There are two restrictions: First, any country is contiguous, there are no exclaves. The second restriction is that countries need to have a common border; if they only touch in a point, they can be colored with the same color. Even though Kempe's proof was wrong, he used some of the ideas which would later permit a correct proof.
In the 1960s and 1970s, Heinrich Heesch developed a first sketch of a proof by computer. Kenneth Appel and Wolfgang Haken improved this sketch in 1976 . They were able to reduce the number of cases that would need to be tested to 1936; a later version was made that relied on testing only 1476 cases.  Each case needed to be tested by a computer .

In 1996, Neil Robertson, Daniel Sanders, Paul Seymour and Robin Thomas improved the method, and reduced the number of cases to be tested to 663. Again, each case needed to be tested by computer. 

In 2005, Georges Gonthier and Benjamin Werner developed a formal proof. This was an improvement, because it allowed to use theorem-proving software, for the first time. The software used is called Coq.
The four color theorem is the first big mathematical problem that was proved with the help of a computer. Because the proof cannot be done by a human, some mathematicians did not recognize it as correct. To verify the proof, it is necessary to rely on a correctly working software and hardware to validate the proof. Because the proof was done by computer, it is also not very elegant.

Attempts that turned out to be wrong 
The four color theorem has been notorious for attracting a large number of false proofs and disproofs in its long history. At first, The New York Times refused to report on the Appel–Haken proof. The newspaper did this as a matter of policy; it feared that the proof would be shown false like the ones before it .  
Some proofs took a long time, till they could be falsified: For Kempe's and Tait's proofs falsifying them took over a decade.
The simplest counterexamples generally try to create one region which touches all the others. This forces the remaining regions to be colored with only three colors. Because the four color theorem is true, this is always possible; however, because the person drawing the map is focused on the one large region, they do not notice that the remaining regions can in fact be colored with three colors.

This trick can be generalized: If the colors of some regions in a map are chosen beforehand, it becomes impossible to color the remaining regions in such a way that in total, only four colors are used. Someone verifying the counterexample may not think that it may be needed to change the color of these regions. This will make the counterexample look valid, even though it is not.
Perhaps one effect underlying this common misconception is the fact that the color restriction is not transitive: a region only has to be colored differently from regions it touches directly, not regions touching regions that it touches. If this were the restriction, planar graphs would require arbitrarily large numbers of colors.

Other false disproofs violate the assumptions of the theorem in unexpected ways, such as using a region that has multiple disconnected parts, or not allowing regions of the same color from touching at a point.
Coloring political maps
In real life, many countries have exclaves or colonies. Since they belong to the country, they need to be colored with the same color as the parent country. This means that usually, more than four colors are needed to color such a map. When mathematicians talk about the graph associated with the problem, they say that is not planar. Even though it is easy to check if a graph is planar, finding the fewest number of colors needed to color it is very difficult. It is NP-complete, which is one of the most difficult problems that exist. The fewest number of colors needed to color a graph is known as its chromatic number. Many of the problems that happen when trying to solve the four color theorem are related to discrete mathematics. For this reason, methods from algebraic topology are often used.
Extension to "non-flat" maps
The four color theorem requires the "map" to be on a flat surface, what mathematicians call a plane. In 1890, Percy John Heawood created what is called Heawood conjecture today: It asks the same question as the four color theorem, but for any topological object. As an example, a torus can be colored with at most seven colors. The Heawood conjecture gives a formula that works for all such objects, except the Klein bottle.

References

Articles and Books 
 
 
 
 
 
 
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 Chechulin V. L. About а one proof of a planar's graphs 4-chromatically http://www.uresearch.psu.ru/files/articles/17_89592.doc

Mentioned in this article

Other websites
:WikiBooks:Famous Theorems of Mathematics/Four color theorem

Combinatorial optimization
Mathematical theorems
Graph theory
A theorem is a proven idea in mathematics. Theorems are proved using logic and other theorems that have already been proved. A minor theorem that one must prove to prove a major theorem is called a lemma. Theorems are made of two parts: hypotheses and conclusions. 

Theorems use deduction, in contrast to theories which are empirical.

Some theorems are trivial, since they directly follow from the propositions. Other theorems are called "deep", because their proof is long and difficult. Sometimes, such proofs involve other areas of mathematics or show connections between different areas. A theorem might be simple to state and yet be deep. An excellent example is Fermat's Last Theorem, and there are many other examples of simple yet deep theorems in number theory and combinatorics (among other areas).
There are other theorems for which a proof is known, but cannot be easily written down. Among the best examples are the four color theorem and the Kepler conjecture. Both of these theorems are only known to be true by reducing them to a computational search which is then verified by a computer program. At first, many mathematicians did not accept this form of proof, but it has become more widely accepted over the years. The mathematician Doron Zeilberger has even gone so far as to claim that these are possibly the only nontrivial results that mathematicians have ever proved. Many mathematical theorems can be reduced to simpler computations, including polynomial identities, trigonometric identities and hypergeometric identities.

Related pages 

 Proposition

References

Books
Triceratops was a huge herbivorous ceratopsid dinosaur from the late Cretaceous. Its name came from having three horns on its head. They were mainly found in North America. As adults, they grew up to  long by  tall, and probably weighed around . Fully-grown, their skull was enormous (two meters long and nearly a meter wide). 

Triceratops was a low browser with a bony beak in front of its jaws. The jaws had close-set grinding teeth. Its defence had to stand up to attacks from taller theropods, hence the bony shield which covered its neck. Holes made by teeth have been found on the bony frill behind the horns, and on the sacrum (the part of the spine above the pelvis).
Many fossils of Triceratops have been collected since the genus was first described in 1889. There is at least one complete individual skeleton. Paleontologist John Scannella observed: "It is hard to walk out into the Hell Creek Formation and not stumble upon a Triceratops weathering out of a hillside". Forty-seven complete or partial skulls were discovered in just that area during the decade 2000–2010. Specimens showing life stages from hatchling to adult have been found.

Body

Size 
Individual Triceratops were about 7.9 to 9.0 m (26.0–29.5 ft) in length, 2.9 to 3.0 m (9.5–9.8 ft) in height, and 6.1–12.0 tonnes (13,000–26,000 lb) in weight.
Skull 
The most distinctive feature is their large skull, among the largest of all land animals. The largest known skull (specimen BYU 12183) is estimated to have been  in length when complete, and could reach almost a third of the length of the entire animal. It bore a single horn on the snout, above the nostrils, and a pair of horns approximately 1 m (3 ft) long, with one above each eye. Most other ceratopsids had large holes (fenestrae) in their frills, while those of Triceratops were noticeably solid.

Limbs 
Triceratops species were sturdy, with strong limbs and short three-hoofed hands and four-hoofed feet.
The posture of these dinosaurs has long been the subject of some debate. Originally, it was believed that the front legs of the animal had to be sprawling at angles from the thorax, in order to better bear the weight of the head. This stance can be seen in paintings by Charles Knight and Rudolph Zallinger. However, evidence of trackways, and reconstructions of skeletons show that Triceratops and other ceratopsids had an upright stance during normal locomotion, with the elbows flexed and slightly bowed out. The stance was intermediate between fully upright and fully sprawling, similar the modern rhinoceros.

Paleobiology

Although Triceratops are commonly portrayed as herd animals, there is little evidence that they lived in herds.
In 2012, a group of three Triceratops in relatively complete condition, each of varying sizes from a full-grown adult to a small juvenile, were found in Wyoming, near Newcastle. The remains are currently under excavation by paleontologist Peter Larson and a team from the Black Hills Institute. It is believed that the animals were traveling as a family unit, but it remains unknown if the group consists of a mated pair and their offspring, or two females and a juvenile they were caring for. The remains also show signs of predation or scavenging from Tyrannosaurus, particularly on the largest specimen, with the bones of the front limbs showing breakage and puncture wounds from Tyrannosaurus teeth.
For many years, Triceratops finds were known only from solitary individuals. These remains are very common: one palaeontologist reported having seen 200 specimens of T. prorsus in the Hell Creek Formation of Montana, U.S. Similarly, Barnum Brown claimed to have seen over 500 skulls in the field. Triceratops teeth, horn fragments, frill fragments, and other skull fragments are abundant fossils in the latest Upper Cretaceous of western North America. It was the most dominant herbivore of the time. In 1986, Robert Bakker estimated it as making up 5/6ths of the large dinosaur fauna at the end of the Cretaceous.

Triceratops was one of the last ceratopsian genera to appear before the Cretaceous–Paleogene extinction event. The related Torosaurus, and the more distantly related diminutive Leptoceratops, were also present, though their remains are rarely found.

Dentition and diet
Dentition and diet

Triceratops were herbivorous, and because of their low head, their primary food was probably low growth, although they may have been able to knock down taller plants with their horns, beak, and bulk. The jaws were tipped with a deep, narrow beak, good for grasping and plucking.

Triceratops teeth were arranged in groups called batteries, of 36 to 40 tooth columns, in each side of each jaw with 3 to 5 stacked teeth per column, depending on the size of the animal. This gives a range of 432 to 800 teeth, of which only a fraction were in use at any given time (tooth replacement was continuous and occurred throughout the life of the animal). The great size and numerous teeth of Triceratops suggests that they ate large volumes of fibrous plant material, such as palms and cycads.
There has been much speculation over the functions of Triceratops''' head adornments. The two main theories have revolved around use in combat, or display in courtship, with the latter thought now to be the most likely primary function.Triceratops were long thought to have used their horns and frills in combat with predators such as Tyrannosaurus. The idea was discussed first in 1917 and again 70 years later by Robert Bakker.Sternberg C.H. 1917. Hunting dinosaurs in the badlands of the Red Deer River, Alberta, Canada. San Diego, California. There is evidence that Tyrannosaurus did have aggressive head-on encounters with Triceratops, based on partially healed tyrannosaur tooth marks on a Triceratops brow horn and squamosal; the bitten horn is also broken, with new bone growth after the break. Since the Triceratops wounds healed, the Triceratops survived the encounter. Tyrannosaurus is also known to have fed on Triceratops. Evidence for this includes a heavily tooth-scored Triceratops ilium  and sacrum.
In addition to combat with predators using horns, Triceratops are classically shown engaging each other in combat with horns locked. While studies show that such activity would be feasible, if unlike that of present-day horned animals, there is disagreement about whether they did so.

The large frill also may have helped to increase body area to regulate body temperature. A similar theory has been proposed regarding the plates of Stegosaurus, although this use alone would not account for the bizarre and extravagant variation seen in different members of the Ceratopsidae. This observation is highly suggestive of what is now believed to be the primary function, display.
The theory of their use in sexual display was first proposed by Davitashvili in 1961 and has gained increasing acceptance since. Evidence that visual display was important, either in courtship or in other social behavior, can be seen in the fact that horned dinosaurs differ markedly in their adornments, making each species highly distinctive. Also, modern living creatures with such displays of horns and adornments use them in similar behavior. A 2006 study of the smallest Triceratops skull, ascertained to be a juvenile, shows the frill and horns developed at a very early age, predating sexual development and thus probably important for visual communication and species recognition in general.
Paleopathology 
One skull, assigned to Triceratops, has a hole in the jugal bone. It looks like a puncture wound sustained while the animal was still alive.  This is supported by signs of healing that are present in the bone around the supposed wound. When examined closely, the hole in the bone has a diameter that is very similar to diameter of the distal end of a Triceratops horn. This is evidence of competition between individual dinosaurs.Martin A.J. 2006. Introduction to the study of dinosaurs. 2nd ed, Oxford, Blackwell. pg. 299-300. .

 References 

 Other websites 
 Triceratops  (short summary and good color illustration)
 Triceratops For Kids (a fact sheet about the Triceratops'' with activities for kids)
 Smithsonian Exhibit 
Triceratops Skull Picture 

Ornithischia
Ceratopsids
Dinosaurs of North America
A genus is a rank in the biological classification (or taxonomy). It is above species, and below families. A genus can include more than one species. When biologists talk about a genus, they mean one or more species of animals or plants that are closely related to each other.

As with other taxa, the plural is different from other English words because it is a Latin word. 'Genus' is the singular, and 'genera' is the plural form of the word.

When printing the scientific name of an organism, the name is always in italic. A name of species has two parts, with the genus first. For example, in "Felis silvestris", Felis is the genus. The genus name always begins with a capital letter. In "Felis silvestris catus", the third word is the subspecies, which is not often used.
As a common word 
In writing, genus names in Latin may be 'anglicised' to form a common name. For example, the genus Pseudomonas is "pseudomonad" (plural: "pseudomonads"). In practice, most really common animals and plants already have a common name. So instead of saying 'felids', or 'felines', one says 'cats' both for the family pet, and for all the cat family (Felidae).

Taxonomy
The Cretaceous period is the ninth and longest period in the Phanerozoic eon, lasting 80 million years from 145 to 65 million years ago (mya). It followed the Jurassic period, and is the third and last period of the Mesozoic era. After it came the Cainozoic era. 
The Cretaceous period has just two very long epochs:
 Upper Cretaceous 100.5 million years ago (mya) to 65 mya
 Lower Cretaceous 145.5 mya to 100.5 mya.
The Lower Cretaceous at ~45 million years, is the longest epoch in the Phanerozoic eon.

Though famous for its land fauna, the Cretaceous sea level rose much higher than today. North America was partly covered by an epicontinental inland sea, and half of Britain was under water. One account goes as follows: "During the Late Cretaceous (94–64 mya) sea level was up to 650 metres higher than at the start of the Albian, when it was perhaps about the same as it is today... The peak transgressions (sea levels) can be seen world-wide. There were rises of sea level of about 10–90 metres per m.y."
In the Upper Cretaceous, chalk, a type of limestone, was laid down in warm shallow seas. Chalk is 95% to 99% made up of coccoliths, the calcium carbonate (CaCO3) plates which tiny single-celled algae (coccolithophorids) produce.
At its end came the famous meteorite strike which, with the volcanic flood basalts spewed out in the Deccan Plateau (India), ended so many of the dominant life-forms: see K/T extinction event.

References
A textbook is a book used for the study of a subject. People use a textbook to learn facts and methods about a certain subject. Textbooks sometimes have questions to test the knowledge and understanding of the learner.

A workbook is a type of textbook that has only practice questions and exercises. Workbooks are designed not to teach but to provide practice and to highlight areas which need more learning. A revision guide is a type of textbook that is used to remind the learner about the subject and give him/her extra practice, especially before an examination.

A textbook is usually lent to students by a school to accompany a course the school is teaching. Sometimes, especially at university, students have to buy the textbooks they need themselves or borrow them from a library.

Most textbooks are only published in printed format. However, some are now available online as electronic books.

Learning
This means it cannot be proved within the discussion of a problem. So inside some discussion, it is thought to be true. There are many reasons why it has no proof. For example,
 The statement might be obvious. This means most people think it is clearly true. An example of an obvious axiom is the principle of contradiction. It says that a statement and its opposite cannot both be true at the same time and place.
 The statement is based on physical laws and can easily be observed. An example is Newton's laws of motion. They are easily observed in the physical world.
 The statement is a proposition. Here, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. This means the emphasis is on what happens if the axiom is true. Whether the proposition is empirically true is not the goal of logic. This is a more modern definition of an axiom.
Logic can be used to find theorems from the axioms. Then those theorems can be used to make more theorems. This is often how math works. Axioms are important because logical arguments start with them.

Euclid's axioms 
Euclid of Alexandria was a Greek mathematician. Around the year 300 BC, he made the earliest list of axioms which we know of. The following are just a few of them:
 Two numbers that are both the same as a third number are the same number.
 If A and B are two numbers that are the same, and C and D are also the same, A+C is the same as B+D.
 If A and B are two numbers that are the same, and C and D are also the same, A-C is the same as B-D.
 Two shapes that fill exactly the same space are the same shape.
 If you divide a number by anything more than 1, the quotient (result) will be less than the original number.

Related pages 
 Axiom of choice, an axiom in set theory

Notes 

Mathematics
A set is an idea from mathematics. A set has members (also called elements). A set is defined by its members, so any two sets with the same members are the same (e.g., if set  and set  have the same members, then ).

A set cannot have the same member more than once. Membership is the only thing that matters. For example, there is no order or other difference among the members. Anything can be a member of a set, including sets themselves (though if a set is a member of itself, paradoxes such as Russell's paradox can happen).

What to do with sets 

Imagine the set is a bag.

Element of 
Various things can be put into a bag. Later on, a good question would be if a certain thing is in the bag. Mathematicians call this element of. Something is an element of a set, if that thing can be found in the respective bag. The symbol used for this is :

,

which means that  is in the bag  or  is an element of .
Unlike a bag, a set can contain at most one item of a given type. So for a set of fruits, it would make no difference if there is one orange, or if there are 10 oranges.

Empty set 
Like a bag, a set can also be empty. The empty set is like an empty bag: it has nothing in it. The "empty set" is also called the null set and is represented by the symbol .

Universe 
If we consider, say, some sets of American cars, e.g. a set of all Fords and a set of all Dodges, we may also wish to consider the whole set of American cars. In this case, the set of all American cars would be called a universe.

In other words, a universe is a collection of all the elements one wishes to consider in a given problem. The universe is usually named .

Comparing sets 
Two sets can be compared. This is like looking into two different bags. If they contain the same things, they are equal. No matter, in which order these things are.

For example, if  and , the sets are the same.
Cardinality of a set 
When mathematicians talk about a set, they sometimes want to know how big a set is (or what is the cardinality of the set). They do this by counting how many elements are in the set (how many items are in the bag). For finite sets the cardinality is a simple number. The empty set has a cardinality of 0. The set  has a cardinality of 2.

Two sets have the same cardinality if we can pair up their elements—if we can join two elements, one from each set. The set  and the set  have the same cardinality. E.g., we could pair apple with sun, and orange with moon. The order does not matter. It is possible to pair all the elements, and none is left out. But the set  and the set  have different cardinality.
If we try to pair them up, we always leave out one animal.
Infinite cardinality 
At times cardinality is not a number. Sometimes a set has infinite cardinality. The set of all integers is a set with infinite cardinality. Some sets with infinite cardinality are bigger (have a bigger cardinality) than others. There are more real numbers than there are natural numbers, for example, which means we cannot pair up the set of integers and the set of real numbers, even if we worked forever.

Countability 
If you can count the elements of a set, it is called a countable set. Countable sets include all sets with a finite number of members. Countable sets also include some infinite sets, such as the natural numbers. You can count the natural numbers with . The natural numbers are nicknamed "the counting numbers", since they are what we usually use to count things with.
An uncountable set is an infinite set that is impossible to count. If we try to count the elements, we will always skip some. It does not matter what step we take. The set of real numbers is an uncountable set. There are many other uncountable sets, even such a small interval like .[3]

Subsets 

If you look at the set  and the set , you can see that all elements in the first set are also in the second set. We say:  is a subset of 
As a formula it looks like this:

In general, when all elements of set  are also elements of set , we call   a subset of :
.
It is usually read " is contained in ."

Example: Every Chevrolet is an American car. So the set of all Chevrolets is contained in the set of all American cars.

Set operations 

There are different ways to combine sets.

Intersections 
The intersection  of two sets  and  is a set that contains all the elements that are both in set  and in set  at the same time.
Example: When  is the set of all cheap cars, and  is the set of all American cars, then  is the set of all cheap American cars.

Unions 

The union  of two sets  and  is a set that contains all the elements that are in set  or in set .
This "or" is the inclusive disjunction, so the union also contains the elements, that are in set  and in set .
By the way, this means, that the intersection is a subset of the union:
.

Example: When  is the set of all cheap cars, and  is the set of all American cars, then  is the set of all cars, without all expensive cars that are not from America.

Complements 
Complement can mean two different things:

 The complement of  is the universe  without all the elements of :
 
The universe  is the set of all things you speak about.
Example: When  is the set of all cars, and  is the set of all cheap cars, then C is the set of all expensive cars.

 The set difference of  and  is the set  without all the elements of :
It is also called the relative complement of  in  .
Example: When  is the set of all cheap cars, and  is the set of all American cars, then  is the set of all expensive American cars.

If you exchange the sets in the set difference, the result is different:In the example with the cars, the difference  is the set of all cheap cars, that are not made in America.

Notation 
Most mathematicians use uppercase ITALIC (usually Roman) letters to write about sets (such as , , ). The things that are seen as elements of sets are usually written with lowercase Roman letters.

One way of showing a set is by a list of its members, separated by commas, included in braces.
For example,
  is set which has members 1, 2, and 3.