A Balancing Act: Dice, Dominos, Turtles and the Gömböc

The shape of an object determines whether it stands, topples, or rights itself. Starting from familiar examples such as dice and dominos, this lecture introduces the idea of stable and unstable equilibria of rigid bodies under gravity. It then turns to the amazing quest of finding a convex homogeneous body with a single stable equilibrium point and shows how the humble turtle uses mathematics to find its way in life.