Colloquium

Dmitry Ryabogin, Kent State University

"On bodies floating in equilibrium in every orientation"

We give a negative answer to Ulam's Problem 19 from the Scottish Book asking is a solid of uniform density which will float in water in every position a sphere? Assuming that the density of water is 1, we show that there exists a strictly convex body of revolution K\subset {\mathbb R^3} of uniform density \frac{1}{2}, which is not a Euclidean ball, yet floats in equilibrium in every orientation.

MC 5501