# Geometry Fun

## Four Color Map Puzzle

The four color theorem says that you only need four colors to color any normal map so that no bordering regions have the same color. The proof was so hard it required a computer. Can you color this blank map using only four colors? Try it before you look at the solution (by clicking the image). Puzzle from Martin Gardner.

## Möbius Strip

Make a Möbius strip by taking a strip of paper, giving it a half twist, and taping the ends together. Now cut it in half the long way. It's surprising. Make another Möbius strip and cut it in thirds the long way. It's also surprising. Try different numbers of twists and different numbers of cuts.

## Turning a Sphere Inside-out

Can you smoothly turn a sphere inside-out, conceptually allowing the surface
to intersect itself, but never allowing any sharp creases? Steve Smale
proved it could be done. Bill Thurston invented this non-optimal but very
beautiful method. These images are from the animation *Outside
In*, copyright © The
Geometry Center, University of Minnesota.