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Ultimate stability

The Gömböc is an object with a very specific trick: no matter how much you push it or tip it over, it will always return to the same position.


Domokos [Public domain], via Wikimedia Commons

Let’s talk about points of equilibrium. A cube has six equilibrium points: if it’s sitting on a flat surface, there are six different stable orientations. You could technically balance a cube on one of its edges, but one tiny push and it falls into one of the stable orientations. (The technical term for this precarious balance, by the way, is an unstable point of equilibrium.) Almost every shape in the world has several stable points of equilibrium. Almost.

In the 1990s, the Russian mathematician Vladimir Igorevich Arnold worked out that it was theoretically possible to construct an object that had only one stable point of equilibrium. In 2006, a couple of Hungarian scientists (Péter Várkonyi and Gábor Domokos) found it for real.

The Gömböc cannot be tipped over. Put it in any position and it will rock back and forth and eventually return to that one stable position. Technically speaking, it has only one stable point of equilibrium, and only one extra unstable point of equilibrium. There are other objects with the one stable equilibrium point, but they typically have several unstable points compared to the Gömböc’s one.

This is such a big deal that authentic Gömböcs have been donated to universities, libraries, and museums around the world. There’s one at the university where I work.

The shape of the Gömböc resembles that of an Indian Star Tortoise, which has led some people to hypothesize that evolution has selected for this shape so that the tortoise is difficult to tip over and can easily right itself.

Categories: Mathematics & statistics Sciences

The Generalist

I live in Auckland, New Zealand, and am curious about most things.

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