Is a convex plane body determined by an isoptic?
type: Item
instance of: scholarly article
title: Is a convex plane body determined by an isoptic?
zbMATH Open document ID: 1235.52005
author: Árpád Kurusa
published in: Beiträge zur Algebra und Geometrie
publication date: 2012-02-29T00:00:00Z
full work available at URL: bodyisop.pdf
review text: The set of points from which a (planar) convex body \(B\) is seen under a constant angle \(\nu\in(0,\pi)\) is called the \(\nu\)-isoptic of \(B\). This paper refers to the question when a (planar) convex body is determined by a \(\nu\)-isoptic of it. The author derives uniqueness results for ellipses, for special angles, for convex polygons and for rotationally symmetric convex bodies. In particular, it is shown that two planar convex bodies coincide if they have an isoptic with the same \(\nu\in (0,\pi)\) in common, where \(1-{\nu\over\pi}\) is irrational or rational with even numerator in its lowest terms, and that in the remaining cases two convex polygons with common isoptic coincide, and a common isoptic of two different rotationally symmetric convex bodies is a circle.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 52A38
zbMATH DE Number: 6010054
zbMATH Keywords: isoptic
zbMATH Keywords: inner isoptic
zbMATH Keywords: geometric tomography
zbMATH Keywords: support function
zbMATH Keywords: ellipses
zbMATH Keywords: convex body
MaRDI profile type: Publication
OpenAlex ID: W2040965718
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DOI: 10.1007/S13366-011-0074-2
description: scientific article; zbMATH DE number 6010054