The Four Color Problem

The "four color problem" is a simple and yet quite significant problem in mathematics, with implications for thinking about human understanding generally. Some of these history, significance and implications of the four color problem will be explored in the present exhibit, which is currently under development. For the moment, background information can be obtained from several other web exhibits

• The Most Colorful Math of All, from MEGA mathematics at Los Alamos National Laboratory
• Four-Color Theorem, from Eric Weisstein's Treasure Trove of Mathematics
• Maps of Many Colors, from Ivars Peterson's MathLand
• Four Color Theorem, by Robin Thomas et al., Georgia Tech
• The Four Color Problem and its Connection to South Arican Flora, by Ostrid Oellermann, University of Winnipeg

The Shockwave movie below makes it possible for you to play with the four color problem yourself. Create a "map of countries" of any number, shape, and size by drawing in the space, or let Serendip create a map for you by clicking on the Generate Map button. The question is how many colors are required to color such a map, using the rule that no two countries with adjacent borders may be the same color (countries meeting at a point may be the same color).

Once generated, either by you or by Serendip, click on Submit Map. After a processing delay, Serendip will then present the map to you in grey, and you can color individual countries by clicking on them (or let Serendip color the map for you). See if you can create a map that requires two colors, or three colors, or four colors. If you create one that requires five colors, you will upset mathematicians (and a few others) worldwide.

Created by Paul Grobstein and Sasha Schwartz. Shockwave programming by Sasha Schwartz. Reactions, comments, suggestions gratefully received. Get the Shockwave plug-in. (Update: additional help with running Shockwave)