Build a uniform solid, no weighted bottom, that always rights itself — possible?
A weighted roly-poly toy always pops back upright because it's bottom-heavy. Could a convex shape made of a single uniform material, with no hidden weights and no flat faces, do the same thing purely through its geometry, with only one stable resting position? For decades this seemed like it might be impossible.
Reveal the answer
Yes. In 2006, mathematicians Gábor Domokos and Péter Várkonyi proved such a shape exists, with exactly one stable and one unstable equilibrium, and built the first physical model, naming it the Gömböc. It confirmed a 1995 conjecture by mathematician Vladimir Arnold, and the shape later turned out to explain how some tortoises right themselves after landing on their backs.