Cornell recently received a unique gift — known as a “gömböc” — that bears the gratitude of a visiting scholar and showcases the fascinating possibilities of mathematics.
Prof. Gábor Domokos, mechanics, materials and structures, Budapest University of Technology and Economics, gave the University a gömböc, which was placed in the Math Library on Thursday.
It has exactly one stable and one unstable point of equilibrium. In layman terms, that means that, no matter how it is initially positioned, a gömböc will return to the same stable point when put on a flat surface.
The gömböc — named from the Hungarian word for sphere “gömb” — is inscripted with the number 1865, the year Cornell was founded. The Hungarian professor, who spent two years at Cornell as a Fulbright Fellow and later as an adjunct professor in mechanical and aerospace engineering, said that his gift is expressing his gratitude for the time he spent at Cornell.
In fact, the gömböc played a significant part in Domokos’s career, who spent almost a decade working on proving the existence of a gömböc, a problem proposed by Russian mathematician Vladimir Arnold who hypothesized in 1995 that a convex homogeneous bodies with less than four equilibrium points may exist.
“At some point we went into holidays with my wife, and I convinced her that we should look at pebbles, [hoping] that maybe we will find a gömböc-shaped pebble, and we examined 2,000 pebbles on the beach,” Domokos told The Sun.
His exhausting effort paid off in 2006 when he managed to prove the existence of a gömböc with Péter Várkonyi, his colleague at Budapest University of Technology and Economics.
When he finally proved the existence of the gömböc in 2006, Domokos said it was a “game-changer,” given the difficulty of proving its existence and the potential applications of the shape.
Unlike other self-correcting objects such as the Weeble, which contains weights that make it have a non-uniform density, the gömböc has a uniform density, so it is harder for the shape to have the same self-correcting properties.
It’s also much harder to make a gömböc, according to Domokos. For a gömböc the size of the one currently at Cornell, if the measurements are off by 1/100th of a millimeter, the object will not retain its properties, Domokos said.
“It is very difficult to produce the engraved number because then you remove a small amount of material, so you may have to re-design the whole shape so that it is balanced,” he said.
The gömböc shape is also related to problems in partial differential equations and in convex geometry. It poses interesting questions in both in pure and applied mathematics, Domokos told The Sun. The shape has provided many inspirations for solutions to problems in other fields, such as deducing the provenance of pebbles on Mars by using their shape.
Many near-gömböc shapes can be found in nature: most beach pebbles, for example, have just two stable and two unstable equilibrium points. However, natural shape evolution does not produce true gömböcs, Domokos said.
He hopes that Gömböc 1865 will inspire more students to get interested in mathematics.
“This is a rather beautiful thing and I hope that students would just get curious when they look at it,” Domokos said.