The "Comeback Kid" is a wooden toy with an intriguing property: No matter which way you set it down—on its head, for example, or on its side—it turns itself upright. Two factors account for this: the object's shape, and the fact that the bottom of the toy is heavier than the top.Mathematicians Gábor Domokos of the Budapest Institute of Technology and Economics and Péter Várkonyi of Princeton University wondered if they could make an improved version that wouldn't require the weight at the bottom to right itself. Could the shape of the object alone be enough to pull it upright?
Eventually, the team managed to construct an object mathematically that has just one stable and one unstable balance point (slightest breeze would knock it over). 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.
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.
It sounds like a tempting challenge, but there is a catch: Domokos and Várkonyi are guessing that a self-righting polyhedron would have many thousands of sides. So the prize might only amount to a few pennies.
Link & Image: Mathtrek
Tags: Self-righting | Object | Mathematics
Comments