# Four Color Theorem

(Difference between revisions)
 Revision as of 14:26, 3 June 2009 (edit)← Previous diff Revision as of 14:54, 3 June 2009 (edit) (undo)Next diff → Line 1: Line 1: {{Image Description {{Image Description |ImageName=Four Color |ImageName=Four Color - |Image=Usagraphfinal.PNG + |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=Algebra + |Field=Graph Theory |InProgress=Yes |InProgress=Yes }} }}

## Revision as of 14:54, 3 June 2009

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