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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.
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Once the pair had built their Once the pair had built their self-righting object, they noticed that it looked very much like a turtle. They figured that wasn’t an accident, since it would be useful for a turtle never to get stuck on its back., they noticed that it looked very much like a turtle. They figured that wasn’t an accident, since it would be useful for a turtle never to get stuck on its back.
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The mathematicians still face an unanswered question. The self-righting objects they’ve found have been smooth and curvy. They wonder if it’s possible to create a self-righting polyhedral object, which would have flat sides. They think it is probably possible, but they haven’t yet managed to find such an object. So, they are offering a prize to the first person to find one: $10,000, divided by the number of sides of the polyhedron.