In a café in present-day Lviv, a group of Polish mathematicians collected problems before World War II, many of which are still open. Now at least one thing could be solved – it’s about floating bodies.
Anyone who has ever played water polo in a swimming pool knows the phenomenon: if you don’t grab the floating ball properly, the ball slips away, spinning on any axis on the water surface. Because he can swim stably in any position, no matter where his north pole is. It’s different with a tree trunk, for example: if you place it upright in the water, it will immediately tip back into its normal, flat swimming position. But what about other objects? Are there shapes that are not spheres and can still be oriented in any way in the water?