Geometry Fun
Four Color Map Puzzle
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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 this solution. Puzzle from Martin Gardner.
Turning a Sphere Inside-out
Can you smoothly turn a sphere inside-out, 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.