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On Poncelet's porism

Waldemar CieślakElżbieta Szczygielska — 2010

Annales UMCS, Mathematica

We consider circular annuli with Poncelet's porism property. We prove two identities which imply Chapple's, Steiner's and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.

On Poncelet’s porism

Waldemar CieślakElżbieta Szczygielska — 2010

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

We consider circular annuli with Poncelet’s porism property. We prove two identities which imply Chapple’s, Steiner’s and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.

Rotation indices related to Poncelet’s closure theorem

Waldemar CieślakHorst MartiniWitold Mozgawa — 2014

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with n- gons for any n > k.

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