Journal of Shanghai University(Natural Science Edition) ›› 2014, Vol. 20 ›› Issue (6): 769-777.doi: 10.3969/j.issn.1007-2861.2013.07.030

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Volume of Legendre Ellipsoid of Convex Bodies

HE Shan-sen   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2013-06-05 Online:2014-12-23 Published:2014-12-23

Abstract: A volume formula of the Legendre ellipsoid of convex body is obtained by using two different methods. Also, the volume formula of the Minkowski sum of finite segments is established by using mathematical induction. As applications, the Legendre ellipsoids of several specific convex bodies are calculated and depicted with Matlab.

Key words: Binet ellipsoid, inertia matrix;Matlab, Legendre ellipsoid, Minkowski summation

CLC Number: