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== '''[[Four color theorem]]''' ==
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<small>
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
==Footnotes==
|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&ndash;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;" | &nbsp;[[Four color theorem#References|notes]]
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</small>

Latest revision as of 10:19, 11 September 2020

Napoleon (Napoleon Bonaparte or, after 1804, Napoleon I, Emperor of the French) was a world historic figure and dictator of France from 1799 to 1814. He was the greatest general of his age--perhaps any age, with a sure command of battlefield tactics and campaign strategies, As a civil leader he played a major role in the French Revolution, then ended it when he became dictator in 1799 and Emperor of France in 1804 He modernized the French military, fiscal, political legal and religious systems. He fought an unending series of wars against Britain with a complex, ever-changing coalition of European nations on both sides. Refusing to compromise after his immense defeat in Russia in 1812, he was overwhelmed by a coalition of enemies and abdicated in 1814. In 1815 he returned from exile, took control of France, built a new army, and in 100 days almost succeeded--but was defeated at Waterloo and exiled to a remote island. His image and memory are central to French national identity, but he is despised by the British and Russians and is a controversial figure in Germany and elsewhere in Europe.

The Trail of Napoleon - J.F. Horrabin - Map.jpg

Rise to Power

Once the Revolution had begun, so many of the aristocratic officers turned against the Revolutionary government, or were exiled or executed, that a vacuum of senior leadership resulted. Promotions came very quickly now, and loyalty to the Revolution was as important as technical skill; Napoleon had both. His demerits were overlooked as he was twice reinstated, promoted, and allowed to collect his back pay. Paris knew him as an intellectual soldier deeply involved in politics. His first test of military genius came at Toulon in 1793, where the British had seized this key port. Napoleon, an acting Lieutenant-Colonel, used his artillery to force the British to abandon the city. He was immediately promoted by the Jacobin radicals under Robespierre to brigadier-general, joining the ranks of several brilliant young generals. He played a major role in defending Paris itself from counter-revolutionaries, and became the operational planner for the Army of Italy and planned two successful attacks in April 1794. He married Josephine (Rose de Beauharnais) in 1796, after falling violently in love with the older aristocratic widow.[1]

Footnotes
  1. ↑ Englund pp 63-73, 91-2, 97-8

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