A generalization of the discrete isoperimetric inequality for piecewise smooth curves of constant geodesic curvature
type: Item
instance of: scholarly article
title: A generalization of the discrete isoperimetric inequality for piecewise smooth curves of constant geodesic curvature
zbMATH Open document ID: 1136.51014
published in: Periodica Mathematica Hungarica
publication date: 2008-05-29T00:00:00Z
review text: In the geometries of constant curvature, the isoperimetric problem is well-known. That is, the maximal area polygon is regular if the number of vertices and its perimeter are given. In this article, the authors study its extension, considering polygons with circular arcs (with given radius) instead of polygons with geodesic edges. This is a kind of tickling problems in the plane geometry. Unfortunately the result is the same (that is, the regular polygon gives the maximal area.) Technically, they consider the configuration space with such circular polygons and solve the first derivatives.
reviewed by: Kazushi Ahara
Mathematics Subject Classification ID: 51M10
Mathematics Subject Classification ID: 51M16
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 5281484
zbMATH Keywords: isoperimetric inequality
zbMATH Keywords: Euclidean plane
zbMATH Keywords: hyperbolic plane
zbMATH Keywords: spherical geometry
author: Balázs Csikós
author: Zsolt Lángi
author: Márton Naszódi
MaRDI profile type: Publication
full work available at URL: s10998-006-0026-z
OpenAlex ID: W2016419337
DOI: 10.1007/S10998-006-0026-Z
description: scientific article; zbMATH DE number 5281484