Meet the Gömböc: The world's first self-righting object
The Gömböc was invented by Hungarian mathematicians, and is the world's only artificial, self-righting shape. It's what's called a mono-monostatic shape, and was born of a mathematical theory. After ten years of work, detailed design programs, and hundreds of tests with rocks of different types, the scientists proved the theory right and the Gömböc was born.
With no power the Gömböc is a consistent weight all the way through. It has a wide curve on the bottom, surrounded by flatish sides and a ridged curve of a top.
No matter how it's placed on a flat surface, it will right itself. The mathematical theory stated that a self-righting shape was possible, and that it had one stable point of balance, and one unstable point. Placing it on the curve on its top will let it pick itself up quickly. Placing on its flat side starts a slower process. It rolls back and forward slowly, then slows almost to a stop, then rolls back and forward quickly in a tiny vibrating motion, and then falls onto its stable point of balance, righting itself again.
Gömböcs are not really attractive and could be mistaken for children's toys. However, nothing could be further from a children's toy. The different angles and proportions have to be measured to within ten microns – one tenth of the thickness of a human hair - to make the shape work. If you wish to buy one they are very expensive. What must be appreciated is math and the ingenious scientists who for many years of examining rocks who finally made their breakthrough one fateful day.