Tuesday 9 January 2007 — This is almost 18 years old. Be careful.
At dinner the other night, our table wobbled. While the waitress fetched a wedge to stabilize it, I told my fellow diners about an applicable mathematical proof: If the legs of a table are even, but the table wobbles because of an uneven floor surface, then rotating the table will always find a position where all four legs are touching the ground.
They were skeptical, but it is true. The ground must be continuous, in the theory of functions sense: no cliff-like changes in height. As proof, here’s an intuitive thought experiment, and the same concept, but full of mind-bending rigor which I don’t understand.
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Paul Downs
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