On Measures of Symmetry of Convex Bodies

Abstract

Let K be a convex body (compact, convex set with interior points) in n-dimensional Euclidean space En, and let V(K) denote the volume of K. Let K′ be a centrally symmetric body of maximum volume contained in K (in fact, K′ is unique; see 2 or 9), and definec(K) = V(K′)/V(K)Letc(n) = inf{c(K) : K ⊂ En}.