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== '''[[ | == '''[[Four color theorem]]''' == | ||
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The ''' | The '''four color theorem''', sometimes known as the '''four color map theorem''' or '''Guthrie's problem''', is a [[problem]] in [[cartography]] and [[mathematics]]. It had been noticed that it only required four [[color]]s to fill in the different [[contiguous]] [[shape]]s on a [[map]] of regions or [[country|countries]] or [[province]]s in a flat surface known as a [[plane (geometry)|plane]] such that no two [[adjacent]] regions with a common [[boundary]] had the same color. But proving this [[proposition]] proved extraordinarily difficult, and it required [[analysis]] by high-powered [[computer]]s before the problem could be solved. In mathematical history, there had been numerous attempts to prove the supposition, but these so-called [[proof (mathematics)|proofs]] turned out to be flawed. There had been accepted proofs that a map could be colored in using more colors than four, such as six or five, but proving that only four colors were required was not done successfully until 1976 by mathematicians Appel and Haken, although some mathematicians do not accept it since parts of the proof consisted of an analysis of [[discrete]] cases by a computer.<ref name=Math1>{{cite news | ||
|title= Four-Color Theorem | |||
|publisher= Wolfram MathWorld | |||
|quote= Six colors can be proven to suffice for the g=0 case, and this number can easily be reduced to five, but reducing the number of colors all the way to four proved very difficult. This result was finally obtained by Appel and Haken (1977), who constructed a computer-assisted proof that four colors were sufficient. However, because part of the proof consisted of an exhaustive analysis of many discrete cases by a computer, some mathematicians do not accept it. However, no flaws have yet been found, so the proof appears valid. A shorter, independent proof was constructed by Robertson et al. (1996; Thomas 1998). | |||
|date= 2010-04-18 | |||
|url= http://mathworld.wolfram.com/Four-ColorTheorem.html | |||
|accessdate= 2010-04-18 | |||
}}</ref> But, at the present time, the proof remains viable, and was confirmed independently by Robertson and Thomas in association with other mathematicians in 1996–1998 who have offered a simpler version of the proof, but it is still complex, even for advanced mathematicians.<ref name=Math1/> It is possible that an even simpler, more elegant, proof will someday be discovered, but many mathematicians think that a shorter, more elegant and simple proof is impossible. | |||
''[[Four color theorem|.... (read more)]]'' | |||
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! style="text-align: center;" | [[ | ! style="text-align: center;" | [[Four color theorem#References|notes]] | ||
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Revision as of 23:27, 23 March 2013
Four color theorem
The four color theorem, sometimes known as the four color map theorem or Guthrie's problem, is a problem in cartography and mathematics. It had been noticed that it only required four colors to fill in the different contiguous shapes on a map of regions or countries or provinces in a flat surface known as a plane such that no two adjacent regions with a common boundary had the same color. But proving this proposition proved extraordinarily difficult, and it required analysis by high-powered computers before the problem could be solved. In mathematical history, there had been numerous attempts to prove the supposition, but these so-called proofs turned out to be flawed. There had been accepted proofs that a map could be colored in using more colors than four, such as six or five, but proving that only four colors were required was not done successfully until 1976 by mathematicians Appel and Haken, although some mathematicians do not accept it since parts of the proof consisted of an analysis of discrete cases by a computer.[1] But, at the present time, the proof remains viable, and was confirmed independently by Robertson and Thomas in association with other mathematicians in 1996–1998 who have offered a simpler version of the proof, but it is still complex, even for advanced mathematicians.[1] It is possible that an even simpler, more elegant, proof will someday be discovered, but many mathematicians think that a shorter, more elegant and simple proof is impossible.
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