A characterization of constant width in Minkowski planes
type: Item
instance of: scholarly article
title: A characterization of constant width in Minkowski planes
zbMATH Open document ID: 1071.52001
author: Gennadiy Averkov
author: Horst Martini
published in: Aequationes Mathematicae
publication date: 2004-11-05T00:00:00Z
review text: Generalizing a result of \textit{A. Heppes} [Mat. Lapok 10, 133--135 (1959; Zbl 0086.15402)], the authors show that a convex body \(K\) in a Minkowski plane has constant Minkowskian width, if and only if every chord of \(K\) splits \(K\) into two parts, one of which has diameter equal to the length of the chord. They also show that the `only if' part can be generalized to higher dimensions.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 2113894
zbMATH Keywords: constant width
zbMATH Keywords: Minkowski plane
zbMATH Keywords: chord length
reviewed by: Wolfgang Weil
MaRDI profile type: Publication
full work available at URL: s00010-003-2723-5
OpenAlex ID: W15814062
DOI: 10.1007/S00010-003-2723-5
description: scientific article; zbMATH DE number 2113894