The week before Christmas break my teacher told me about this theorem. Since then I've been wondering: How many colors would be required for a map in 3 space?
Here are a few stupid solutions to the problem:
n space requires 2n colors
1 space requires 2 colors
2 space requires 4 colors
3 space requires 6 colors
n space requires 2^n colors
1 space requires 2^1 colors
2 space requires 2^2 colors
3 space requires 2^3 colors
3 space requires infinitely many colors.
Does anyone have a good idea for the answer to this question?