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Family Ties: Relating Poncelet 3-Periodics by their Properties (2012.11270v3)
Published 21 Dec 2020 in math.MG, cs.CG, and cs.RO
Abstract: We compare loci types and invariants across Poncelet families interscribed in three distinct concentric Ellipse pairs: (i) ellipse-incircle, (ii) circumcircle-inellipse, and (iii) homothetic. Their metric properties are mostly identical to those of 3 well-studied families: elliptic billiard (confocal pair), Chapple's poristic triangles, and the Brocard porism. We therefore organized them in three related groups.