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Optimizing Area and Perimeter of Convex Sets for Fixed Circumradius and Inradius

Research paper by Károly Böröczky Jr., María A. Hernández Cifre, G. Salinas

Indexed on: 01 Feb '03Published on: 01 Feb '03Published in: Monatshefte für Mathematik



Abstract

 In this paper two problems posed by Santaló are solved: we determine the planar convex sets which have maximum and minimum area or perimeter when the circumradius and the inradius are given, obtaining complete systems of inequalities for the cases (A, R, r) and (p, R, r).