Brunn-Minkowski Theory and Cauchy's Surface Area Formula. Issue 10 (1st December 2017) - Tsukerman, Emmanuel; Veomett, Ellen
Abstract: We use Brunn-Minkowski theory and well-known integration tools to prove Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension. Using the same technique, we give a straightforward extension to intrinsic moment vectors of a convex body.