# Going in Circles: Variations on the Money-Coutts Theorem

Research output: Contribution to journalArticle

4 Citations (Scopus)

### 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.

Original language English (US) 201-209 9 Geometriae Dedicata 80 1-3 Published - Dec 1 2000

### Fingerprint

Circle
Angle
Tangent line
Polygon
Theorem
Incircle or inscribed circle
Triangle
Arc of a curve
Money
Class

### All Science Journal Classification (ASJC) codes

• Geometry and Topology

### Cite this

@article{9bed751afcc44aea900a865dc1634a64,
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",
month = "12",
day = "1",
language = "English (US)",
volume = "80",
pages = "201--209",
journal = "Geometriae Dedicata",
issn = "0046-5755",
publisher = "Springer Netherlands",
number = "1-3",

}

In: Geometriae Dedicata, Vol. 80, No. 1-3, 01.12.2000, p. 201-209.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Going in Circles

T2 - Variations on the Money-Coutts Theorem

AU - Tabachnikov, Serge

PY - 2000/12/1

Y1 - 2000/12/1

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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VL - 80

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JO - Geometriae Dedicata

JF - Geometriae Dedicata

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