Gömböc

A Gömböc is an unusual object. What is so special about it? It is a convex three-dimensional object which, when resting on a flat surface, has one stable and one unstable point of equilibrium only, a highly unusual feature. This means that if you put a Gömböc down on a flat surface, it will always come back to the same resting position at the stable equilibrium position. This can also be described as  it being self-righting.

The existence of this object was conjectured by the Russian mathematician Vladimir Arnold in 1995.

There were many doubts that Gömböcs actually existed due to the fact that there was no such shape in two-dimensions. For example, “an n-sided polygon has n stable equilibrium points — the centres of its sides — and n unstable ones — its vertices.” The best solution in two dimensions is an ellipse, which has two unstable and two stable points of equilibrium.

However, in 2006 Gábor Domokos and Péter Várkonyi proved that this object could exist. Although the shape of such object is not unique, the most famous solution is an egg-like shape with sharp edges.

“The fact that no-one could imagine a three-dimensional shape with just one pair of equilibrium points suggested that it would be worthwhile to disprove its existence… I tried to do this, unsuccessfully, for a very long time. Then I had a conversation with Vladimir Arnold, in which he expressed the view that such a shape might exist after all, despite all the rumours going around that it didn’t. This made me think in a different way, and I soon realised that the problem was much more beautiful than I had thought at first.”

-Domokos

Sources: 1 | 2 | 3

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3 comments

1. Nice article. I would like to underline that the Gomboc should be homogeneous. Without this condition it would be easy to build an object with only one stable and one unstable equilibrium, for example a sphere shaped object with the center of mass shifted from the geometrical center.

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