(auto): These days, Kellogg’s cereals have Disney wobblers in them. Because of their round bottoms and a very low center of gravity, they wobble but end up standing upright.

Unistable polyhedra

Monday 29 August 2005This is 20 years old. Be careful.

These days, Kellogg’s cereals have Disney wobblers in them. Because of their round bottoms and a very low center of gravity, they wobble but end up standing upright. I was discussing this with Max, who had lots of questions about center of gravity. Could you make an object with a center of gravity on the ground? No, because some of the mass has to be on the other side of any line drawn through the center of gravity.

Then I remembered something I’d read about a long time ago. A few searches, and I found it: a unistable polyhedron is one which will only rest on one of its faces. Robert Dawson calls them by a different name, but has some nice pictures: monostatic polytopes.

In the real world, there’s a very pragmatic reason to be concerned about polyhedral stability: it is at the heart of the issue of Fair Dice.

Comments

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Regarding the center of gravity on the ground, boats are a fairly analogous situation and perhaps a good place to take the conversation; they take on ballast to lower their center of gravity which in turn increases their stability and so on...

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