An introduction to a mathematical perspective on coloring the regions or countries of a map. The central problem is to try to use a few colors as possible to color the regions, yet not use so few that the regions aren't easily distinguished from one another.
Learn a simple procedure for making complicated-looking maps that, believe it or not, are always easy to color with only two colors.
Asking yourself why this procedure always seems to produce 2-colorable maps is an invitation to explore
the idea of mathematical proof, as well as to make and color some interesting maps.
Do you think it is possible to draw a map that forces you to use 5 colors when you color it? Wolfgang Haken and Kenneth Appel wrote a computer program that was thousands of lines long to try and find out if you could. According to the results of their program, it isn't possible to draw such a map. But that hasn't kept some very clever kids from trying to find out if there might be some possibility that their program missed. Check out these maps that they have made!
Also, remember that finding a simple proof of the 4 Color Theorem, (one that won't take a computer 1200 hours to complete) is still one of the greatest open problems in mathematics today.
