You can push it, press it or even place it upside down – no matter how hard you try, this oddly-shaped self-righting shape simply will always spring right back up. And that, in a nutshell, is the claim to fame of the Gömböc which, for all practical purposes, looks a little like an egg with sharp edges.
What truly sets a Gömböc apart from every other whimsical shape in the world is that it has only two points of equilibrium. One of these points is stable, and if a Gömböc is placed on a flat surface, resting on this stable equilibrium point, it will keep returning to this point even if you push it around a little.
Placing the Gömböc on its other unstable point of equilibrium is like balancing a pencil on its sharpened tip – even the slightest nudge can cause it to topple over. In addition to these two, it is quite impossible to balance it on any other point.
Despite your best efforts, it will start rolling until it reaches its stable equilibrium point. This is why the Gömböc is described as a self-righting mechanism.
A FIRST UNLIKE ANY OTHER
The concept of self-righting objects has been around for a while now. A sphere that has been weighted such that its center of gravity moves away from its geometric center is a self-righting object as is the very popular ComeBack Kid or roly-poly child we all played with as children.
In the latter case, the lower center of mass combined with the shape of the object to create a ‘righting motion’, which always keeps these objects standing upright. However, none of these objects are homogenous; by their very structure, the density of the material they are made of varies from one point to another.
The idea of a homogenous, convex and three-dimensional self-righting shape was first theorized by the Russian mathematician – Vladimir Arnold, who unfortunately, couldn’t quite derive the shape or the underlying mathematical theory that would enable the creation of such a shape.
It was important that the shape was convex, which would not allow the Gömböc to bulge inwards and which would ensure that a line connecting any two points on the Gömböc would like entirely within the Gömböc.
Creating a non-convex shape is far easier, which was the entire reason why the researchers were so insistent on convexity. And so, the search continued until 2006, when Gábor Domokos and Péter Várkonyi arrived at a solution that has curved edges and looks a little like a sphere with a squashed top.
ROOTED IN NATURE
The complexity of mathematically theorizing a Gömböc led Domokos to seek answers in Nature. While on a holiday to a Greek island, he and his wife inspected nearly 20,000 pebbles in a bid to uncover one that would behave like they wanted it to. When this quest proved futile, Domokos turned his sights to pet stores… more specifically, he began to inspect tortoises.
Realizing that being turned on their backs is a potentially disastrous turn of events for tortoises – males in some species have been known to flip their competitors on their backs when vying for female attention – he began to frequent pet stores and zoos, flipping tortoises on their backs when their owners weren’t looking.
And then, he found the first tortoise that behaved just like his hitherto-hypothesized Gömböc, which was the proverbial Eureka moment in his quest.
IMPLICATIONS OF THE GÖMBÖC
True to the animals that galvanized its creation, the discovery of the Gömböc could prove advantageous to biologists, who will use their understanding of it to delve deeper into the evolution of shell shapes among tortoises.
Domokos is currently developing ways of determining the habitat of tortoises based on the shape of their shells – a process that will help researchers to learn more about the living spaces of extinct species who are only known to researchers by their fossilized shells. Domokos has also used the Gömböc model to explain why asteroids, which have sharp edges and flat areas, evolve the way they do.
Although the Gömböc is currently being produced only for aesthetic purposes – and you can purchase your very own Gömböc too on this website – further practical applications of this research have yet to be uncovered. In the meanwhile, if you happen to be in and around Cambridge, do stop by the Whipple Museum of the History of Science to view the Gömböc that was donated by Domokos and Várkonyi.
Gömböc – The Beauty of Thinking – Márton Szirmai – GE FOCUS FORWARD