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Super awesome cheap ballSaturday 8 August 2009 On a road trip a few months back, we stopped at a gas station on the Mass Pike (the Massachusetts Turnpike for you out-of-staters), and were just idly looking over the cheap junk they had for sale there. A interestingly geometric ball caught my eye. It was green, and had a strange structure that seemed like it would move in some way. I tried pulling gently at its panels but nothing happened. Then I tossed it lightly and caught it: now it was orange! Look: Even after you've tried it a few times, it's still a bit startling to see a sphere turn inside out and still be a sphere. This ball entertained us for the whole weekend, and since it had only cost me $4 at a gas station, we dubbed it Super Awesome Cheap Ball, in homage to Super Happy Fun Ball. A later stop at the gas station unearthed the name of the ball, and its creator: Switch Pitch, by Chuck Hoberman, the creator of the familiar Hoberman Sphere.
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Even after you've tried it a few times, it's still a bit startling to see a sphere turn inside out and still be a sphere.
Although maybe not as startling as cutting up a sphere into pieces and then using the pieces to re-assemble them into two spheres each the same size as the original sphere:
http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
That's a great theorem, but unfortunately, completely impervious to intuition. In the case of Switch Pitch, you can actually see it happening!
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