Gömböc

Remember the toy Comeback Kid? Weeble? Or maybe you called it roly-poly toy? You know, that little guy who stood back up on his round bottom every time, no matter how you pushed it. That was because he had a weighted sphere (his bottom was much heavier and from a different material, therefore, he was inhomogeneous) and a very low center of mass. He actually had a stable point of equilibrium.

In 1995, world-famous Russian mathematician Vladimir Igorevich Arnold proposed that a class of convex, homogeneous bodies, which, when resting on a flat surface have only one stable and only one unstable point of equilibrium, must exist. (In unstable equilibrium, the body will fall out of equilibrium no matter how you push it). A few years later in 2006, his idea was proven by Hungarian scientists, Gábor Domokos and Péter Várkonyi, by constructing a physical example. Meet Gömböc.

Gömböc is basically one of the cutest superstars of mathematics. Its name comes from gömb, which means “sphere” in Hungarian. But there is actually a Hungarian folk tale about an anthropomorphic thing called Gömböc that swallows several people, then explodes in the end as it rolls down a hill because of its weight.

Gömböc made quite an entrance into the scientific world. Since its discovery, scientists have examined its relationship to animals (such as the unusually-shaped Indian star tortoise), pebbles, rocks, engineering applications (drone-cages, Gömböc-shaped capsules for insulin, etc.), and even astronomy (the shape of a certain asteroid has been evaluated based on the mathematics behind Gömböc). And the list continues to grow. Gömböc also inspired award-winning movies and short films as well.

Individual Gömböc models have been in production since 2007. Each model carries a unique serial number. “Gömböc 001” for example, was presented by the creators Domokos and Várkonyi and was sent to Vladimir Arnold as a gift for his 70th birthday. For all the other Gömböces, there is an official Gömböc Map for tracking their location.

So in a nutshell, Gömböc is cool, Hungarians are proud of it greatly. So naturally, they made a 4.5-ton statue replica of the shape. Besides its weight, there is also one interesting fact about it: The Gömböc statue is designed in a way that its length reaches 4851 millimeters at the temperature of 97 degrees Fahrenheit (36 degrees Celsius) because of thermal expansion. This is because 4851 is the 97th extactic number, and such numbers appeared in the work of Professor Arnold on the generalization of the four-vertex Theorem, which is also closely tied to the Gömböc shape.

Besides its function as a tourist attraction, the world’s largest Gömböc statue stands next to a Nokia Skypark office building in order to raise attention to the scientific activities carried out in the area.