An extremal property of the hypersphere

Source abstract

It was shown by Sas (1) that, if K is a plane convex body, then it is possible to inscribe in K a convex n -gon occupying no less a fraction of its area than the regular n -gon occupies in its circumscribing circle. It is the object of this note to establish the n -dimensional analogue of Sas's result, giving incidentally an independent proof of the plane case. The proof is a simple application of the Steiner method of symmetrization.