Family Ties: Relating Poncelet 3-Periodics by their Properties

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Authors Ronaldo Garcia, Dan Reznik arXiv ID 2012.11270 Category math.MG Cross-listed cs.CG, cs.RO Citations 17 Venue KoG Last Checked 3 months ago
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.
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