A Mathematical Comparison: The Two and Four Color Theorems
The following note may be useful to professors and undergraduate students at Christian colleges who would like to think about a simplified proof of the four color theorem. In coloring a geographical map it is customary to give different colors to any two countries which share a border. The four color theorem says that every possible TWO DIMENSIONAL MAP can be colored by using a maximum of FOUR DIFFERENT COLORS.
1. How about a ONE DIMENSIONAL MAP? Try drawing a one dimensional map which is made up of one dimensional countries. Can every possible one dimensional map be colored by using a maximum of TWO DIFFERENT COLORS?
2. Are there any special cases for which a one dimensional map requires more than two colors?
3 Is there a relationship between the REQUIREMENT for four colors in a two dimensional map with two dimensional countries and the REQUIREMENT (?) for two colors in a one dimensional map with one dimensional countries?
4. Is there any physical or mathematical interpretation that can be given to the CONCEPT OF COLOR in the two color theorem? The four color theorem?
The conversational format of this site encourages casual, offhand responses. This is fine in many cases, but it easily leads to sloppy and inappropriate thinking. The apparent simplicity of these questions is deceptive. I personally prefer to communicate with readers who think (for at least a few days) before responding.
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