On symmetric versions of Sylvester's problem

2003/05/28 by Mark W. Meckes
Mathematics · #math.MG #math.PR #msc:50A22 #msc:50A40 #msc:60D05

paper · pdf · doi:10.1007/s00605-005-0300-9

published as Monatsh. Math. 145 no. 4, 307-319 (2005) · AMS-LaTeX

arxiv created 2003/05/28 · arxiv updated 2009/11/30

Abstract

We consider moments of the normalized volume of a symmetric or nonsymmetric random polytope in a fixed symmetric convex body. We investigate for which bodies these moments are extremized, and calculate exact values in some of the extreme cases. We show that these moments are maximized among planar convex bodies by parallelograms.

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