On the length of space curves of constant width
type: Item
instance of: scholarly article
title: On the length of space curves of constant width
zbMATH Open document ID: 0788.53001
author: Eberhard Teufel
published in: Beiträge zur Algebra und Geometrie
publication date: 1994-06-12T00:00:00Z
full work available at URL: https://eudml.org/doc/228373
full work available at URL: no.2
review text: The length of a closed space curve of constant width \(d\) is always greater or equal to \(\pi d\) with equality holding exactly in the plane case. Here an upper bound for the length of such a curve is obtained as a multiple of \(d\). The proof uses methods from spherical integral geometry and the fact that there is an isotopy of every closed space curve of constant width to a spherical one such that the constant width and the length are preserved [cf. the reviewer, Math. Nachr. 53, 337-344 (1972; Zbl 0214.203)].
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 510037
zbMATH Keywords: transnormal curve
zbMATH Keywords: length
zbMATH Keywords: spherical integral geometry
reviewed by: Bernd Wegner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 510037