Circles and polygons
type: Item
instance of: scholarly article
title: Circles and polygons
zbMATH Open document ID: 0960.51009
DOI: 10.1023/A:1005265015972
published in: Geometriae Dedicata
publication date: 2001-05-10T00:00:00Z
review text: Let us consider the following sequence of circles in a given triangle \(A_1,A_2,A_3\). The circle \(S_1\) is inscribed in the angle \(A_1\); the circle \(S_2\) inscribed in the angle \(A_2\) and tangent to \(S_1;S_3\) inscribed in the angle \(A_3\) and tangent to \(S_2\); etc. The circle \(S_i\) is smaller than the two circles tangent to \(S_{i-1}\). A nice elementary theorem (Money-Coutts theorem) states that the above process is 6-periodic, i.e. \(S_7=S_1\). The author considers the process for parallelograms and shows that the above process is always preperiodic.
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 1485594
zbMATH Keywords: circles
zbMATH Keywords: polygons
zbMATH Keywords: periodicity
zbMATH Keywords: chaos
zbMATH Keywords: Money-Coutts theorem
zbMATH Keywords: parallelograms
author: Serge Troubetzkoy
reviewed by: Ágota H. Temesvári
MaRDI profile type: Publication
full work available at URL: a:1005265015972
OpenAlex ID: W32346766
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description: scientific article; zbMATH DE number 1485594