Gömböc
A Gömböc [ ˈɡœmbœts ] is a three-dimensional body with only one stable and only one unstable equilibrium position ("mono-monostatic"), which was discovered in 2006 by the Hungarian mathematicians Gábor Domokos and Péter Várkonyi . Its shape resembles a rounded hand ax .
Similar to a stand-up man , the Gömböc always returns to its stable position of equilibrium. In contrast to the stand-up man, in which an additional weight in the spherical lower part shifts the center of gravity , the Gömböc is a convex body with a homogeneous (even) density, which returns to its original position solely through its shape.
Story of discovery
For a long time, mathematicians were interested in whether there was a geometric body with a corresponding property. The mathematician Vladimir Igorewitsch Arnold was the first to suspect the existence of such bodies.
Two Hungarian mathematicians, Gábor Domokos from the Technical and Economic University of Budapest and Péter Várkonyi from Princeton University, devoted themselves to the search for a “homogeneous stand-up man” . The two-dimensional case was considered first. The mathematicians succeeded in proving that every flat figure has at least two stable equilibrium points and two unstable equilibrium points. Further investigations led to three-dimensional bodies, first theoretically, later also practically, the possibility of the existence of the body sought was shown.
Origin of name
The term Gömböc is derived from the Hungarian word gömb for sphere due to its similar shape . In addition, the Hungarian word gömböc on the one hand means “ pressed sausage”, but also stands for “dumplings” or colloquially for “fat”.
Monostatics in nature
There are turtles with an almost monostatic shell, which makes it easier for them to get out of the supine position, such as the Indian star turtle .
literature
- Péter L. Várkonyi, Gabor Domokos: Static equilibria of rigid bodies: Dice, pebbles, and the Poincaré-Hopf theorem ( PDF file, 1.1 MB), Journal of Nonlinear Science 16 No. 3, June 2006, p. 255 –281 doi : 10.1007 / s00332-005-0691-8 (English)
- Péter L. Várkonyi, Gabor Domokos: Mono-monostatic bodies: The answer to Arnold's question ( PDF file, 1.3 MB), The Mathematical Intelligencer 28 No. 4, December 2006, pp. 34–38 doi : 10.1007 / BF02984701 (English)
- Julie Rehmeyer: Can't knock it down , sciencenews.org, 2007 (English)
- Holger Dambeck: The mathematics of the turtle role , Spiegel Online, October 25, 2007
- Gábor Domokos, Péter L. Várkonyi: Geometry and self-righting of turtles , Proceedings of the Royal Society B 275, 2008, pp. 11–17 doi : 10.1098 / rspb.2007.1188 (English)
Web links
- The Gömböc on www.gomboc.eu (English)
- World expos :: Photos :: Shanghai :: Hungary - Presentation of the Gömböc at the World Exhibition 2010 with photos from all sides
swell
- ↑ Várkonyi, Domokos: Static equilibria of rigid bodies: Dice, pebbles, and the Poincaré-Hopf theorem , 2006 (English)
- ↑ Bettina Gartner: Get up again! Gábor Domokos , Time No. 4, January 15, 2009
- ↑ Magyar-Német Nagyszótar (Hungarian-German Large Dictionary)
- ↑ Domokos, Várkonyi: Geometry and self-righting of turtles , 2008 (English)