Minimal ellipsoids and their duals
It is proved that most (in certain sense) convex bodies in the euclidean d-space \(E^ d\) touch the boundaries of their minimal circumscribed and maximal inscribed ellipsoids in precisely \(d(d+3)/2\) points. Related results on compact sets in \(E^ d\) are contained in the paper, too. [Cf. the author, Discrete Geometry and convexity, Ann. N. Y. Acad. Sci. 440, 163-170 (1985; Zbl 0571.52007) and \textit{T. Zamfirescu}, J. Reine Angew. Math. 350, 183-187 (1984; Zbl 0557.52004)].
scientific article; zbMATH DE number 4101989
scientific article