Rotation indices related to Poncelet’s closure theorem
Waldemar Cieślak, Horst Martini, Witold Mozgawa (2014)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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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.