Perfect circles and spheres, the shape of hanging chains, the trajectory of planets and projectiles, the shape of soap bubbles and snowflakes, the forms of planets and galaxies, the formation of rocks and crystals, all have one thing in common: they are all solutions to certain optimization problems, trying to minimize or optimize certain aspects of area, volume or energy in general.
The geometrical basis is – once again – closely related to supershapes. Conic sections at the core, once more.
Spheres, conic sections and power functions are special cases of supershapes. Recent work by Miyuki Koiso and Bennett Palmer used supershapes as examples of surfaces with constant mean curvature for anisotropic energies, giving equilibrium shapes for a wide range of natural shapes.Genicaplab and the Simon Stevin Institute for Geometry are exploring the consequences of these recent findings towards applications in optimization, such as shortest distances in networks and optimal packing.