707 Words3 Pages

Math IA
Four Color Theorem
Matt Reed
Four Color Theorem
I. Introduction
Ever since the beginning of travel and exploration, maps have helped people record the specifics of new and unexplored regions of the earth. The earliest maps were crudely drawn by hand and were rough estimates of geographic area based on interpretation of the land. Once people began coloring maps, to designate partitions within regions, the problem arose regarding the necessary number of colors it would take to color a map.
II. History
The theorem was first proposed by August Ferdinand Moebius in 1840. However, the problem was ignored until 1856. In 1856, Francis Guthrie proposed the conjecture to his brother Frederick who then brought the problem to the attention of his advisor; Augustus De Morgan. From this point on, a series of mathematicians sought to prove that it takes a minimum of four colors to color every region on a map without adjacent regions being the same color.
III. The Theorem
The theorem developed over a series of stages between the 1840s and the 1980s. Multiple false proofs and conjectures were proclaimed in the 1850s. However, they were all eventually disproven. A precursor to the proof, written in 1890 by Heawood, details the use of five colors to shade in the regions of a map. However, the proof involving four colors remained ultimately unproved until the 1970s. The proof was one of the first ever to be proven by a computer, which brought about a revolution in the solutions of mathematical conjectures. Although flawed, Kempe's original purported proof of the four color theorem provided some of the basic tools later used to prove it. Kempe's argument goes as follows. “First, if planar regions separated by the graph are not trian...
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..., numerous renditions of the proof were disproven and built upon. Additionally, the Four Color Theorem was the first proof to be solved with aid from a computational device, creating controversy as to its legitimacy as a proof of its time period. However, now that computers have been integrated into our daily lives, it has become a full-fledged proof that will continue to be in use as long as new places to map are discovered.
Works Cited
O'Connor, JJ, and EF Robertson. "The Four Colour Theorem." The Four Colour Theorem. N.p., Sept. 1996. Web. 04 Feb. 2014.
Rogers, Leo. "The Four Colour Theorem." : Nrich.maths.org. N.p., n.d. Web. 08 Jan. 2014.
Thomas, Robin. "An Update on the Four Color Theorem." AMS.org. N.p., Aug. 1998. Web. 05 Jan. 2014.
Wilson, Robin J. Four Colors Suffice: How the Map Problem Was Solved. Princeton, NJ: Princeton UP, 2002. Print.

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