Steiner symmetrization

Summary

Steiner symmetrization is an operation that turns a convex body into a convex body that is symmetric about a chosen hyperplane. It slides each chord of the body orthogonal to the hyperplane along its line until the hyperplane cuts the chord in its midpoint. The operation keeps the volume, and it does not increase the surface area or the diameter. Repeating it in well chosen directions makes a body converge to a ball, which gives proofs of the isoperimetric inequality and of related extremal results.