Optimizing the perimeter and the area of convex sets with fixed diameter and circumradius
type: Item
instance of: scholarly article
title: Optimizing the perimeter and the area of convex sets with fixed diameter and circumradius
zbMATH Open document ID: 1017.52004
author: Maria A. Hernández Cifre
published in: Archiv der Mathematik
publication date: 2002-12-01T00:00:00Z
review text: The author determines planar convex sets which have minimum area or perimeter when the diameter and the circumradius are prescribed, obtaining the corresponding geometric inequalities. She uses these inequalities to obtain two complete systems of inequalities: systems of inequalities relating all the geometric characteristics such that, for any set of numbers satisfying those conditions, a planar figure with these values of the characteristics exists. She obtains the corresponding Blaschke's diagrams for these complete systems. Such results give a complete answer to two questions posed by Santalo in 1961.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 1837418
zbMATH Keywords: convex sets
zbMATH Keywords: perimeter
zbMATH Keywords: area
zbMATH Keywords: diameter
zbMATH Keywords: circumradius
zbMATH Keywords: inequalities
zbMATH Keywords: complete systems of inequalities
MaRDI profile type: Publication
full work available at URL: s00013-002-8297-y
OpenAlex ID: W2122060136
DOI: 10.1007/S00013-002-8297-Y
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description: scientific article; zbMATH DE number 1837418