Download or read book Symmetry Points of a Convex Set written by Alexandre Belloni and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a convex body S and a point x in S, let sym(x,S) denote the symmetry value of x in S: sym(x,S):= max{t : x + t(x - y) is in S for every y in S}, which essentially measures how symmetric S is about the point x, and define sym(S):=max{sym(x,S) : x in S}. We call x* a symmetry point of S if x* achieves the above supremum. These symmetry measures are all invariant under invertible affine transformation and/or change in norm, and so are of interest in the study of the geometry of convex sets. In this study we demonstrate various properties of sym(x,S), including relations with convex geometry quantities like volume, distance and diameter, and cross-ratio distance. When S is polyhedral of the form {x : Ax