| Popis: |
We introduce various concepts of floating bodies, namely Ulam's floating body, Dupin's floating body, and the convex floating body and we give examples for the different concepts. In particular, we investigate if counterexamples to certain long standing open problems for the one type of bodies can be used for the other. One of the problems is Ulam's problem asking whether spheres are the only solids that can float in equilibrium in every direction. The other one is the homothety problem which asks if a body must be an ellipsoid if it is homothetic to its floating body. While there are partial solutions to these problems, complete solutions still need to be found. |
