An isoperimetric inequality for convex polygons and convex sets with the same symmetrals
type: Item
instance of: scholarly article
title: An isoperimetric inequality for convex polygons and convex sets with the same symmetrals
zbMATH Open document ID: 0579.52007
DOI: 10.1007/BF00149270
author: Marco Longinetti
published in: Geometriae Dedicata
publication date: 1986-01-01T00:00:00Z
review text: Let H and K be two plane compact convex bodies with the same symmetrals in n different directions (n\(\geq 3)\). By using new isoperimetric inequalities for convex polygons it is proved that \((*) meas (H\Delta K) \leq (\ell^ 2/8n)\tan \pi /n,\) where \(\ell\) denotes the length of \(\partial (H\cap K)\). Furthermore it is shown that equality holds in (*) if and only if the directions are equally spaced and H and K are two regular concentric polygons with n sides, each obtained from the other by rotation through an angle \(\pi\) /n.
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 3927802
zbMATH Keywords: Steiner symmetral
zbMATH Keywords: isoperimetric inequalities for convex polygons
zbMATH Keywords: regular concentric polygons
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3927802