Chalmers’ latest installation is a mathematical curiosity that has long fascinated and delighted.
There was a ceremonial atmosphere in the entrance to the Origo building on Friday afternoon as Chalmers President Martin Nilsson Jacobi and Hungary’s Ambassador to Sweden, Péter Palóczi, together – and very carefully – placed the ‘convex mono-monostatic body’ in an illuminated glass display case.
A Gömböc (pronounced ‘gœmbœts’) is a rounded body that always returns to the same position when placed on a flat surface. What makes it special is that it is entirely convex, has a homogeneous density and only two equilibrium points: one stable and one unstable.
It is not entirely easy to describe, or understand, but seeing the Gömböc makes much of it fall into place. (See also the fact box below.)
In 1995, the Hungarian mathematician Vladimir Arnold predicted that such a body could exist.
‘The Gömböc’s unique and elegant shape opens up a wealth of unanswered questions and will inspire and spark curiosity for generations to come,’ said Péter Palóczi.
He also explained that individually numbered Gömböc models have been donated as permanent installations to prestigious universities and cultural institutions around the world since 2007.
‘This is about more than presenting an object. It is a symbol of the cooperation between Chalmers and Hungary, as well as between Hungary and Sweden.’
The turtle principle
The edition is limited and numbered from 1 to the current year, which is presently 2026. Number 1829 had already been taken, so Chalmers’ Gömböc was given the number 1748, after the year in which William Chalmers was born. It is the fourth example in Sweden – after those at the universities in Stockholm, Uppsala and Lund – and the first in Gothenburg.
Martin Nilsson Jacobi expressed his gratitude for the gift.
‘A Gömböc is not only an interesting mathematical object; it is also incredibly beautiful.’
Torbjörn Lundh, Professor of Mathematics, then explained the mathematical background to the Gömböc. To illustrate the principle, he compared the Gömböc to the shell of the Indian star tortoise, whose shape helps the tortoise right itself if it ends up on its back.
While the entrance to the Origo building is being renovated, the Gömböc will temporarily be displayed elsewhere in the building. It will then return to its intended location.
Facts / Gömböc
A Gömböc (pronounced ‘gœmbœts’) is a convex mono-monostatic body with homogeneous density. Its existence was conjectured by the mathematician Vladimir Arnold in 1995, and many mathematicians were initially sceptical that the Gömböc shape could exist. The reason was that a geometric shape with only convex surfaces cannot have just two equilibrium positions in two dimensions.
A mono-monostatic body has only one stable and one unstable equilibrium point when resting on a flat surface. One example is a sphere with a weight along its surface, meaning that the weight always seeks its lowest point. Such a sphere also has one, and only one, unstable equilibrium point, when the weight is at its highest position, and is therefore a mono-monostatic body. What makes a Gömböc so special is that it also has a uniform density and only convex surfaces.
One animal in nature that comes close to having these properties, and whose shape bears a striking resemblance to a Gömböc, is the star tortoise. The shape was created by two mathematicians from Budapest, Péter Várkonyi and Dr Gábor Domokos.
The mathematicians were inspired by a teddy bear that always tips back to its stable point; the Gömböc behaves in the same way.
Source: Wikipedia