The gömböc (Hungarian: [ˈɡømbøt͡s]) is a convex three-dimensional homogeneous body that when resting on a flat surface has just one stable and one unstable point of equilibrium. Its existence was conjectured by the Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by the 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 with a very strict shape tolerance (about one part in a thousand).

The most famous solution, capitalized as Gömböc to distinguish it from the generic gömböc, has a sharpened top, as shown in the photo. Its shape helped to explain the body structure of some tortoises in relation to their ability to return to equilibrium position after being placed upside down.[1][2][3][4] Copies of the gömböc have been donated to institutions and museums, and the largest one was presented at the World Expo 2010 in Shanghai in China.[5][6] In December 2017, a 4.5 m (15 ft) gömböc statue was installed in the Corvin Quarter (Corvin-negyed) in Budapest.[7]

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