Four-Color Problem

Materials: Handouts

Step 1:

¨ Do worksheet "Creativity with Colors" from Activities from the Mathematics Teacher.

¨ How many colors are needed to color a map made with any number of triangles in the plane?

¨ How many colors are needed to color a map made with any number of squares in the plane?

¨ Below I have created a map by drawing a curve that seems to randomly move around the page and then connects back to itself at the beginning. How many colors does it take to color this map? Draw other such maps. Can you draw any conclusions?

¨ Create an algorithm to determine if a map is 2-colorable or not. Test this algorithm on several maps.

¨ Create a map that requires 3 colors. Prove that 2 colors are not enough.

¨ Create a map that requires 4 colors. Prove that 3 colors are not enough.

¨ Find out a little about the history of the Four-Color Problem, i.e., what it is, when and how it was solved.