UW Combinatorics and Geometry Seminar: Dmitry Ryabogin

Let $K$be a convex body made of material of uniform density less than 1 submerged into water of density 1. How to find the directions of equilibrium of $K$? How many directions of equilibrium does a triangular prism have? (A direction $n$orthogonal to the water surface is called the direction of equilibrium if the line passing through the center of mass of $K$and the center of mass of the underwater part is parallel to $n$).