What is a Gömböc?

The ‘Gömböc’ – pronounced as ‘goemboets – is the first known homogenous object with one stable and one unstable equilibrium point, thus two equilibria altogether on a horizontal surface. It can be proven that no object with less than two equilibria exists.

The stable equilibrium (S)

If placed on a horizontal surface in an arbitrary position the Gömböc returns to the stable equilibrium point,  similar to ‘weeble’ toys. While the weebles rely on a weight in the bottom, the Gömböc consists of homogenous material, thus the shape itself accounts for self-righting.

The unstable equilibrium (I)

The single unstable equilibrium point of the Gömböc is on the opposite side. It is possible to balance the body in this position, however the slightest disturbance makes it fall, similar to a pencil balanced on its tip.

The question whether Gömböc-type objects exist or not was posed by the great Russian mathematician Vladimir Igorevich Arnold at a conference in 1995, in Hamburg, during a conversation with Gabor Domokos.

Inventors

Domokos Gábor

Gabor Domokos

Gabor Domokos got his PhD in 1989. Currently he is professor at the Dept. of Mechanics, Materials and Structures at the Technical Uiversity of Budapest. He has been member of the Hungarian Academy of Sciences since 2004. In his inaugural talk, he performed a conversation with Aristoteles on irrational numbers.

He was visiting fellow at the University of Maryland, and he is adjunct professor of Cornell University. He has been collaborating with Philip Holmes in discrete and continuous dynamical systems resarch projects.

His interest include population dynamics and chaos. In his free time he likes free-hand drawing, taking photos and hiking.

Várkonyi Péter

Peter Varkonyi

Peter Varkonyi was a Silver Medalist at the Physics Student Olympiad in 1997. He graduated from the Technical University of Budapest as Architect, in 2003. He got his PhD in 2006, his work was advised by Gabor Domokos.

His research field includes symmetry in engineering structures, biomechanics, evolutionary modeling. In the year 2006/07 he was a Korányi-fellow at Princeton University. Since then, he has been assistant professor in Budapest.

He is married and has five children; nevertheless he has some time for his favourite activities: swimming, sailing and badminton.

Publications

The Mathematical Intelligencer

Mono-monostatic Bodies: The Answer to Arnold's Question

Journal of Nonlinear Science

Static Equilibria of Rigid Bodies: Dice, Pebbles, and the Poincaré-Hopf Theorem

Proceedings B - The Royal Society Publishing

Geometry and self-righting of turtles

Sponsors and partners

Ottó Albrecht

Sponsor of the individual Gömböc donation program to institutions

Co&Co Communications

The logo and design communication of the Gömböc was developed by Co&Co.

Concorde Alapkezelő

The numbered Gömböc pieces could be launched thanks to Concorde Alapkezelő.

Hungarian National Cultural Fund

Sponsor of the educational DVD about Arnold and Gömböc