Isoptics of a closed strictly convex curve. II
type: Item
instance of: scholarly article
title: Isoptics of a closed strictly convex curve. II
zbMATH Open document ID: 0881.53003
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1997-06-16T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108414
review text: [Part I was reviewed in Zbl 0739.53001.] This second part proves several interesting properties of isoptics of plane closed convex curves \(C\). Let \(C_\alpha\) denote the \(\alpha\)-isotopic of \(C\), i.e., the locus of points from which all of \(C\) is seen under the constant angle \(\pi-\alpha\). A Crofton-type integral formula is proved for the annulus enclosed by \(C\) and \(C_\alpha\), and it is used to derive a differential equation for the dependence of the area of this annulus from \(\alpha\). Relations between tangent directions to \(C_\alpha\) and directions of special chords of \(C\) are contained. The preservation of constant width is investigated. Some technical differential equations are derived at the end of the paper. The methods of proof are elementary.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 53C65
zbMATH DE Number: 1021759
zbMATH Keywords: Crofton formula
zbMATH Keywords: closed convex planar curves
zbMATH Keywords: isoptics
zbMATH Keywords: constant width
author: Waldemar Cieślak
author: Andrzej Miernowski
author: Witold Mozgawa
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Q5201844
cites work: Q3840976
cites work: Q3978997
cites work: Q4110292
description: scientific article; zbMATH DE number 1021759