Family Ties: Relating Poncelet 3-Periodics by their Properties
This work provides a new organization for researchers studying Poncelet families by relating them to existing well-studied families.
The paper compares loci types and invariants across three Poncelet families (ellipse-incircle, circumcircle-inellipse, and homothetic) interscribed in concentric ellipse pairs. It finds that their metric properties are mostly identical to three well-studied families: elliptic billiard, Chapple's poristic triangles, and Brocard porism.
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.