Rotation indices related to Poncelet’s closure theorem. (English) Zbl 1312.51005
Summary: Let \(C_{R}C_{r}\) denote an annulus formed by two non-concentric circles \(C_{R}, C_{r}\) in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for \(k\)-gons circuminscribed to \(C_{R}C_{r}\), then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with \(C_{r}\), with \(n\)-gons for any \(n > k\).
MSC:
| 51M04 | Elementary problems in Euclidean geometries |
| 51N20 | Euclidean analytic geometry |
| 52A10 | Convex sets in \(2\) dimensions (including convex curves) |
| 53A04 | Curves in Euclidean and related spaces |
Keywords:
bar billiards; Euler’s triangle formula; Poncelet’s closure theorem; Poncelet’s porism propertyReferences:
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