This note is based on Nicolas Garcia Trillos’ talk, Some Problems and Techniques in Geometric Probability, at Carnegie Mellon University on January 29, 2015. In particular, we demonstrate a probabilistic proof of the isoperimetric inequality. The proof can also be found in Integral Geometry and Geometric Probability by Luis A. Santaló. Theorem. For a convex set… Continue reading A Probabilistic Proof of Isoperimetric Inequality