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) |
|---|---|
| Pages (from-to) | 201-209 |
| Number of pages | 9 |
| Journal | Geometriae Dedicata |
| Volume | 80 |
| Issue number | 1-3 |
| State | Published - Dec 1 2000 |
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All Science Journal Classification (ASJC) codes
- Geometry and Topology
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Going in Circles : Variations on the Money-Coutts Theorem. / Tabachnikov, Serge.
In: Geometriae Dedicata, Vol. 80, No. 1-3, 01.12.2000, p. 201-209.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.
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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 -