#### Title

#### Document Type

Project

#### Publication Date

Spring 2012

#### Keywords

Four color theorem, Mathematics history

#### Abstract

The history of mathematics is pervaded by problems which can be stated simply, but are difficult and in some cases impossible to prove. The pursuit of solutions to these problems has been an important catalyst in mathematics, aiding the development of many disparate fields. While Fermat’s Last theorem, which states *x ^{n} + y^{n} = z^{n}* has no integer solutions for n > 2 and

*x, y, z*≠ 0

^{[12]}is perhaps the most famous of these problems, the Four Color Theorem proved a challenge to some of the greatest mathematical minds from its conception 1852 until its eventual proof in 1976.

The Four Color Theorem was first stated in 1852 by a young English mathematician, Francis Guthrie, who noticed that he could color a map of the counties of England using at most four colors such that no two counties of the same color were touching along a measurable border and from this observation postulated that he could color all maps this way In 1852 there was no formalized field of mathematics which could be drawn on to study the four color theorem, so the first mathematicians to study the four color theorem used two dimensional maps of regions that resemble geographical maps. Using this language a statement of the four color theorem is as follows: for every two dimensional map of regions, the regions of the map can be colored by at most four colors such that no two regions of the same color share a measurable border.

#### Department

Computer Science

#### Recommended Citation

Turner, Patrick, "The Four Color Theorem" (2012). *WWU Honors Program Senior Projects*. 299.

https://cedar.wwu.edu/wwu_honors/299

#### Subjects - Topical (LCSH)

Four-color problem

#### Genre/Form

student projects; term papers

#### Type

Text

#### Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

#### Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

#### Language

English

#### Format

application/pdf