My lecture centers around convex sets of constant width and the biographies of two scientists from the 19th and 20th century, Franz Reuleaux and Stefan Cohn-Vossen. While some of it is at the level of mathematical entertainment (how to drill a square hole?), it will also contain a deep and only partially answered questions and some aspects on the history of mathematics. To be very specific, geometric aspects of the following nonlinear PDE for the boundary of a convex closed set in Euclidean 3-space will be addressed: $\min\{ \kappa_1,\kappa_2\}=1$.