Alternative proof of Sine's theorem on the size of a regular polygon in \(\mathbb{R}{}^ n\) with the \(\ell{}_ \infty\)-metric
type: Item
instance of: scholarly article
title: Alternative proof of Sine's theorem on the size of a regular polygon in \(\mathbb{R}{}^ n\) with the \(\ell{}_ \infty\)-metric
zbMATH Open document ID: 0753.51011
DOI: 10.1007/BF02187853
author: H. A. Wilbrink
author: Aart Blokhuis
published in: Discrete \& Computational Geometry
publication date: 1992-09-26T00:00:00Z
full work available at URL: https://eudml.org/doc/131206
review text: Le \((A,d)\) be a finite metric space with a transitive group of isometries. Furthermore suppose that \((A,d)\) is isometrically embeddable into \(\mathbb{R}^ n\) endowed with the \(l_ \infty\)-norm. The authors show that this implies that \(A\) has at most \((2n)^ n\) elements. Hence every regular \(m\)-gon in \((\mathbb{R}^ n,l_ \infty)\) has at most \((2n)^ n\) vertices.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 51M20
zbMATH DE Number: 54919
zbMATH Keywords: regular polygon
zbMATH Keywords: maximum norm
MaRDI profile type: Publication
cites work: Nonlinear models of diffusion on a finite space
cites work: Omega limit sets of nonexpansive maps: Finiteness and cardinality estimates
cites work: On nonlinear contraction semigroups in sup norm spaces
OpenAlex ID: W2049776615
description: scientific article; zbMATH DE number 54919