The Gömböc

Gömböc - Wikipedia, the free encyclopedia

A gömböc (pronounced [ˈɡømbøts] in Hungarian, sometimes spelled gomboc and pronounced GOM-bock in English) is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. Its existence was conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi. The gömböc shape is not unique; it has countless varieties, most of which are very close to a sphere and all have very strict shape tolerance (about 0.1 mm per 10 cm). The most famous solution has a sharpened top and is shown on the right. Its shape helped to explain the body structure of some turtles in relation to their ability to return to equilibrium position after being placed upside down.[1][2][3][4]

The Living Gömböc | Natural History Magazine

Illustrating the difference between an unstable and a stable equilibrium, a plywood triangle (top), regarded as a two-dimensional object, may balance precariously on one of its three points or come to rest on one of its three long sides. Similarly, a rod with both ends sliced off at oblique angles (middle) teeters on its short side—as it would if stood on either pointed end—but finds stability on its long side. Designed by mathematicians, the Gömböc (bottom) never rests for long on any point except its one and only stable surface.
Illustration by Joe Sharkey

Resembling the Gömböc, the shape of its shell gives an Indian star tortoise only one stable configuration: on its feet!
Illustration by Joe Sharkey