Geometry Fun
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.
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.
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