Convex curves whose points are vertices of billiard triangles
type: Item
instance of: scholarly article
title: Convex curves whose points are vertices of billiard triangles
zbMATH Open document ID: 0646.52002
author: Nobuhiro Innami
published in: Kodai Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: On a smooth convex curve of constant width all points are vertices of periodic orbits of billiard balls with period two. On ellipses every point is a vertex of a billiard n-gon for all \(n\geq 3\). The author shows that the converse is not true if the assumption is restricted to \(n=3\). More precisely, smooth convex curves are constructed which are different from an ellipse such that all points are vertices of billiard triangles, i.e. vertices of orbits of period three.
Mathematics Subject Classification ID: 52A10
Mathematics Subject Classification ID: 53A04
zbMATH DE Number: 4054462
zbMATH Keywords: billiard n-gons
zbMATH Keywords: geometrical optics
zbMATH Keywords: convex curves
zbMATH Keywords: vertices of billiard triangles
zbMATH Keywords: vertices of orbits of period three
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138038814
OpenAlex ID: W2081339264
cites work: Q3814339
cites work: \(C^\infty\)-approximation of continuous ovals of constant width
DOI: 10.2996/KMJ/1138038814
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description: scientific article; zbMATH DE number 4054462