A Gömböc is a mathematics-based shape discovered in 2007, solved after a decade of several mathematicians trying to prove its existence. It was discovered by two mathematicians in Hungary, in 2007.
A Gömböc is a convex, three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. It is the world’s first self-righting object and has won several accolades, including the New York Times’ acknowledgement as one of the best ideas of 2007.
If you put a Gömböc down on a flat surface, resting on its stable equilibrium point, it will stay in the same position. "Even if you kick it a little, it will come back to its resting position at the stable equilibrium point," says Gábor Domokos, one of the inventors of Gömböc. "If it is put down at a non-equilibrium point it will start rolling around in a systematic way until it has reached the stable equilibrium position. In other words, the Gömböc is self-righting."
Here's a link to the article, courtesy of MapleSoft. Its software was used in the mathematical computations that flushed the elusive Gömböc out of hiding.
Oh yeah, there's even an official Gömböc web store where you can buy one.....