Gomboc
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A Gomboc (Hungarian: Gömböc) is an artificial three-dimensional shape with one stable and one unstable point of equilibrium, enabling it to mimic the "self-righting" abilities of shelled animals such as turtles and beetles. Such a shape was conjectured by Russian mathematician Vladimir Arnold as a mono-monostatic body – a convex, homogeneous body with fewer than four equilibria.
The shape was developed by Gabor Domokos (head of Mechanics, Materials and Structures at Budapest University of Technology and Economics in Hungary) and a former student of his, Peter Varkonyi (at Princeton University). The Gomboc made the front page of mathematical journal The Mathematical Intelligencer.[1]
Domokos and his wife developed a classification system for shapes based on their points of equilibrium by collecting pebbles from a beach and noting their equilibrium points. The Gomboc was developed in conjunction with that system as a supposed "perfect" self-righting mechanism.[2]
"Gömb" in Hungarian means "sphere" and "gömböc" refers to a sphere-like object. The mathematical Gömböc has indeed sphere-like properties. In particluar its flatness and thinnes are minimal, and this is the only type of nondegenerate object with this property. The sphere has also minimal flatness and thinness, however, it is degenerate.(cf. Várkonyi & Domokos, 2006.)
[edit] References
- ^ Varkonyi, P.L., Domokos, G.: Mono-monostatic bodies: the answer to Arnold's question. The Mathematical Intelligencer, 28 (4) pp 34-38.(2006.)
- ^ Gergely, Andras: Boffins develop a 'new shape' called Gomboc, The Age (via Reuters), February 13, 2007.
