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Perfectly relaxing, perfectly inspirational.
The perfect body with the perfect shape.

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„A shape whose impossibility might have been an elegant theorem, but whose existence may be much more elegant.” Chandler Davis

What is Gömböc?

The 'Gömböc' (pronounced: '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.

Why so special?

Although the study of the number and location static equilibrium points of rigid bodies dates back to Archimedes, one of the most fundamental questions, the minimal number of equilibrium points, remained open until very recently. While there were strong indications that this minimal number should be 4, one of the greatest mathematicians of the 20th century, Vladimir Igorevich Arnold, thought otherwise and suggested in 1995 that the minimal number may be 2. This conjecture baffled many scientists sine no one had ever seen an object with just 2 equilibrium points. However, as in many other cases, Arnold’s conjecture turned out to correct: ten years later two Hungarian engineers first proved the existence of such objects and subsequently also built a physically functioning shape which they dubbed “Gömböc.” The first functioning Gömböc (with individual serial number 001) was donated in Moscow, on August 20th 2007 by the inventors to Arnold, on the occasion of his 70th birthday. Here, upon receiving Gömböc 001, Arnold offered further thoughts connecting the Gömböc to natural sciences.

Although he did not live to know, Arnold was once again proved to be right: the Gömböc shape appears to be deeply encoded into Nature. For instance, pebbles, as they abrade, reduce their number of equilibrium points and thus, in this sense, they evolve towards a Gömböc, although it is extremely unlikely that any pebble would ever reach this ultimate goal. Using this theory, scientists can draw wide-ranging conclusions on the history of an abraded pebble or rock – based alone on its shape. If you are interested in further fun facts about Gömböc, stay updated and follow our blog for news!

You can find more information about the background of this unique mathematical innovation at www.gomboc.eu.

Why buy one?

Gömböc is a mathematical innovation, exclusive gift and science toy, that can help you think over your dilemmas, draw your daily inspiration and remind yourself: it’s just a matter of time to regain your balance. Different versions of Gömböc are available from steel, bronze, aluminium, plexiglass and from a unique black substance in our science webshop. This self-righting shape is a perfect gift for your business partners, colleagues and friends.

Inspired by

Vladimir I. Arnold

Vladimir I. Arnold

The Origin of the Idea
The question whether Gömböc-type objects exist or not was posed by the great Russian mathematician Vladimir I. Arnold at a conference in 1995, in a conversation with Gabor Domokos. Arnold is considered to be one of the most influential scientists of the 20th century. While he is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, he made important contributions in several areas including dynamical systems theory, catastrophe theory, topology, algebraic geometry, symplectic geometry, differential equations, classical mechanics, hydrodynamics and singularity theory, including posing the ADE classification problem, since his first main result—the solution of Hilbert's thirteenth problem in 1957 at the age of 19. Arnold is also known as a popularizer of mathematics. Source: Wikipedia. You can find out more about Arnold and the Gömböc here: www.gomboc.eu/99.pdf

Inventors

Gábor Domokos

Inventor
Gabor Domokos got his PhD in 1989. Currently, he is professor the Dept. of Mechanics, Materials and Structures at the Technical University of Budapest. He has been a member of the Hungarian Academy of Sciences since 2004. In his inaugural talk, he performed a conversation with Aristotle on irrational numbers. He was a 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 research projects. His interests include population dynamics and chaos theory. In his free time he likes free-hand drawing, photographing and hiking.

Péter Varkonyi

Inventor
Péter Várkonyi 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 modelling. In the year 2006/07 he was a Korányi-fellow at Princeton University. Now he is associate professor at the Technical University of Budapest. He is married and has five children; nevertheless he has some time for his favorite activities: swimming, sailing and badminton.

Webshop

“Gömböc helps me to draw my daily inspiration and remind myself: it’s just a matter of time to regain my balance.”

Special designs

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Personalization is not a problem nowadays. However, our webshop has to cope with some difficulties in case of Gömböc, because every hundredth of millimeter counts for Gömböc-type of objects, so we work at very high accuracy levels. The smallest change in the process can cause a harmful result that the product will lose its functionality. Therefore, if we engrave a Gömböc, we have to recalculate the whole self-righting shape to be able to balance the mass inequalities.
Despite these technological challenges, you can order personalized products in new size, made of a new material and with special engraving. If required, it is also possible to develop a special Gömböc with the help of the inventors, which has never been created before and will never be created afterwards.
Customized Gömböcs can be ordered here.

„the geometry of the equilibrium”

"Gömböc is like a mythological creature. It’s recalling me the story of the griffon bird."
Cedric Villani

„An amazing body” / „Verblüffender Körper”

"First homogeneous self-rightning shape."

"One of the most interesting ideas of year 2007"

Press & Media

Gömböc constantly receives growing attention from all around the world. It earned an ever-growing special reputation in science, but our goal is to bring Gömböc closer to everyone, similarly to the career of the Rubic's cube.

We buy pet rocks, snuggies, and shrinky-dinks; mathematicians have Klein bottles, Mobius strips, and the ultimate mathematical novelty item, the Gömböc.

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Other articles

The Gömböc is a roundish piece of clear synthetic material with gently peaked, organic curves. It looks like a piece of modern art. But if you tip it over, something unusual happens: it rights itself

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The Gömböc: The object that shouldn't exist
A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed…

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