Rotation indices related to Poncelet’s closure theorem

Abstract

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.