Mike Beversluis

Monday, April 09, 2007

Tipping Point

Can't Knock It Down
Julie J. Rehmeyer

Eventually, Domokos and Várkonyi managed to prove mathematically that for any flat shape, there are at least two stable balance points and at least two unstable balance points.

Next, the pair began to investigate whether all three-dimensional shapes have at least two stable and two unstable balance points. They tried to generalize their two-dimensional proof to higher dimensions, but it didn't hold up. Therefore, it seemed possible that a self-righting three-dimensional object could exist. Such a shape would have only one stable and one unstable balance point.

They looked for objects in nature that might have such a property. While Domokos was on his honeymoon in Greece, he tested 2,000 pebbles to see if he could find one that would right itself, but none did. "Why he is still married, that is another thing," Várkonyi says. "You need a special woman for this."

I wonder about the stability of marriages to mathematicians. All of the number theorists I have met have been significantly eccentric, but married none the less.

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