Four Color Theorem
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{{Image Description | {{Image Description | ||
|ImageName=Four Color | |ImageName=Four Color | ||
- | |Image= | + | |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? | ||
- | 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. | + | 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. |
- | + | |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 | ||
- | |Field= | + | |Field=Graph Theory |
|InProgress=Yes | |InProgress=Yes | ||
}} | }} |
Revision as of 15:54, 3 June 2009
Four Color |
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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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