Some global properties and constructions for closed curves in the plane
type: Item
instance of: scholarly article
title: Some global properties and constructions for closed curves in the plane
zbMATH Open document ID: 0641.53002
DOI: 10.1007/BF00572448
published in: Geometriae Dedicata
publication date: 1989-01-01T00:00:00Z
review text: \textit{W. Cieslak} and \textit{W. Mozgawa} [ibid. 24, 221-228 (1987; Zbl 0629.53004)] proved several theorems on special pairs of points on rosettes (arc pairs, antipodal pairs, perimeter dividing normals). Here it is shown that most of the results presented there can be extended to very general classes of closed curves by using different methods of proof. Furthermore the notion of rosettes of constant width is discussed in more detail and some classical constructions for convex curves of constant width are generalized to them.
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 4044619
zbMATH Keywords: arc pairs
zbMATH Keywords: antipodal pairs
zbMATH Keywords: perimeter dividing normals
zbMATH Keywords: closed curves
zbMATH Keywords: rosettes of constant width
author: Bernd Wegner
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: On rosettes and almost rosettes
cites work: Self-parallel curves.
cites work: Parallel Immersions in Euclidean Space
cites work: Constant Breadth Curves in the Plane
cites work: Planar Line Families. II
cites work: Q5515051
cites work: Transnormale Isotopien und transnormale Kurven
description: scientific article; zbMATH DE number 4044619