Pleasing Shapes for Topological Objects

Topology is the study of deformable shapes; to draw a picture of a topological object one must choose a particular geometric shape. One strategy is to minimize a geometric energy, of the type that also arises in many physical situations. The energy minimizers or optimal shapes are also often aesthetically pleasing. This article first appeared in an Italian translation [Sullivan, Affascinanti forme per oggetti topologici, 145–156 (2011)].