### Abstract

Given a polygon A_{1},..., A_{n}, consider the chain of circles: S_{1} inscribed in the angle A_{1}, 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. 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 |

State | Published - Dec 1 2000 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

### Cite this

*Geometriae Dedicata*,

*80*(1-3), 201-209.

}

*Geometriae Dedicata*, vol. 80, no. 1-3, pp. 201-209.

**Going in Circles : Variations on the Money-Coutts Theorem.** / Tabachnikov, Serge.

Research output: Contribution to journal › Article

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.

UR - http://www.scopus.com/inward/record.url?scp=0042226854&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042226854&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042226854

VL - 80

SP - 201

EP - 209

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1-3

ER -