Going in Circles: Variations on the Money-Coutts Theorem

Serge Tabachnikov

doi:10.1023/a:1005204813246

Going in Circles: Variations on the Money-Coutts Theorem

Serge Tabachnikov

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Given a polygon A₁,..., A_n, consider the chain of circles: S₁ inscribed in the angle A₁, S₂ inscribed in the angle A₂ and tangent to S₁, S₃ inscribed in the angle A₃ and tangent to S₂, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts theorem.

Original language	English (US)
Pages (from-to)	201-209
Number of pages	9
Journal	Geometriae Dedicata
Volume	80
Issue number	1-3
DOIs	https://doi.org/10.1023/a:1005204813246
State	Published - 2000

All Science Journal Classification (ASJC) codes

Geometry and Topology

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10.1023/a:1005204813246

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title = "Going in Circles: Variations on the Money-Coutts Theorem",

abstract = "Given a polygon A1,..., An, consider the chain of circles: S1 inscribed in the angle A1, S2 inscribed in the angle A2 and tangent to S1, S3 inscribed in the angle A3 and tangent to S2, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts theorem.",

author = "Serge Tabachnikov",

year = "2000",

doi = "10.1023/a:1005204813246",

language = "English (US)",

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TY - JOUR

T1 - Going in Circles

T2 - Variations on the Money-Coutts Theorem

AU - Tabachnikov, Serge

PY - 2000

Y1 - 2000

N2 - Given a polygon A1,..., An, consider the chain of circles: S1 inscribed in the angle A1, S2 inscribed in the angle A2 and tangent to S1, S3 inscribed in the angle A3 and tangent to S2, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts theorem.

AB - Given a polygon A1,..., An, consider the chain of circles: S1 inscribed in the angle A1, S2 inscribed in the angle A2 and tangent to S1, S3 inscribed in the angle A3 and tangent to S2, etc. We describe a class of n-gons for which this process is 2n-periodic. We extend the result to the case when the sides of a polygon are arcs of circles. The case of triangles is known as the Money-Coutts theorem.

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JF - Geometriae Dedicata

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ER -

Going in Circles: Variations on the Money-Coutts Theorem

Abstract

All Science Journal Classification (ASJC) codes

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