Four Color Theorem

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{{Image Description
{{Image Description
|ImageName=Four Color
|ImageName=Four Color
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|Image=Usagraphfinal.PNG
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|Image=Usagraphfinal2.PNG
|ImageIntro=Four coloring and graph representation of the United States.
|ImageIntro=Four coloring and graph representation of the United States.
|ImageDescElem=How many colors are needed to color the territories of a map, if all the territories that share a border must be of different colors?
|ImageDescElem=How many colors are needed to color the territories of a map, if all the territories that share a border must be of different colors?
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It turns out that only four colors are needed to color such a two-dimensional map. It has taken over a century for a correct proof of this fact to emerge, and the proof can currently only be carried out with the aid of computers.
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It turns out that only four colors are needed to color such a two-dimensional map. It has taken over a century for a correct proof of this fact to emerge, and the proof can currently only be carried out with the aid of computers. An example of a map colored with only 4 colors is the map of The United States on this page's main image.
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|ImageDesc=Map coloring is an application of Graph Theory, the study of graphs. A graph is informally a collection of points, known as vertices, connected by lines, known as edges. This p
|AuthorName=Brendan John
|AuthorName=Brendan John
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|Field=Algebra
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|Field=Graph Theory
|InProgress=Yes
|InProgress=Yes
}}
}}

Revision as of 14:54, 3 June 2009

Image:inprogress.png

Four Color

Four coloring and graph representation of the United States.


Basic Description

How many colors are needed to color the territories of a map, if all the territories that share a border must be of different colors?

It turns out that only four colors are needed to color such a two-dimensional map. It has taken over a century for a correct proof of this fact to emerge, and the proof can currently only be carried out with the aid of computers. An example of a map colored with only 4 colors is the map of The United States on this page's main image.

A More Mathematical Explanation

Map coloring is an application of Graph Theory, the study of graphs. A graph is informally a collect [...]

Map coloring is an application of Graph Theory, the study of graphs. A graph is informally a collection of points, known as vertices, connected by lines, known as edges. This p




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