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Family Ties: Relating Poncelet 3-Periodics by their Properties

12/21/2020

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by Ronaldo Garcia, et al.

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We study the dynamic geometry, loci, and invariants of three Poncelet families associated with three distinct concentric Ellipse pairs: with-incircle, with-circumcircle, and homothetic. Most of their properties run parallel to those of 3 well-studied families: elliptic billiard (confocal pair), Chapple's poristic triangles, and the Brocard porism, allowing us to organize them in three "similar" groups.

Ronaldo Garcia
32 publications
Dan Reznik
39 publications

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