Optimizing area and perimeter of convex sets for fixed circumradius and inradius
type: Item
instance of: scholarly article
title: Optimizing area and perimeter of convex sets for fixed circumradius and inradius
zbMATH Open document ID: 1022.52004
author: Guillermo Salinas
author: Károly jun. Böröczky
published in: Monatshefte für Mathematik
publication date: 2003-05-04T00:00:00Z
review text: The authors determine the planar convex sets with fixed values of their circumradius and inradius that either maximize or minimize the area (also the perimeter). The corresponding geometric inequalities are explicitly obtained. Using these new inequalities jointly with the classical inequalities concerning these geometric magnitudes, the authors build complete systems of inequalities for the cases \((A,R,r)\) and \((p,R,r)\); these problems were posed by Santaló in 1961.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 1903790
zbMATH Keywords: geometric inequalities
zbMATH Keywords: complete systems of inequalities
zbMATH Keywords: extremum problems
zbMATH Keywords: area
zbMATH Keywords: perimeter
zbMATH Keywords: inradius
zbMATH Keywords: circumradius
MaRDI profile type: Publication
full work available at URL: s00605-002-0486-z
OpenAlex ID: W2040217759
DOI: 10.1007/S00605-002-0486-Z
description: scientific article; zbMATH DE number 1903790