On highly eccentric cones

Abstract

This paper addresses the issue of estimating the largest possible eccentricity in the class of proper cones of R n. The eccentricity of a proper cone is defined as the angle between the incenter and the circumcenter of the cone. This work establishes also various geometric and topological results concerning the concept of eccentricity.

Centers and partial volumes of convex cones II. Advanced topics

“…Non-eccentricity is a geometric property Table 1 Largest observed value (second row) and expected value (third row) of θ(K) n = 3 n = 4 n = 5 n = 10 n = 15 n = 20 0.1988 π 0.2239 π 0.2409 π 0.2479 π 0.2492 π 0.2497 π 0.0528 π 0.0720 π 0.0829 π 0.1025 π 0.1089 π 0.1127 π studied in depth in the references Henrion and Seeger (2011) and Seeger and Torki (2013). The following proposition is a nontrivial result borrowed from (Seeger and Torki 2013, Theorem 2.2).…”