Family Ties: Relating Poncelet 3-Periodics by their Properties
Metric Geometry
2021-07-14 v3 Computational Geometry
Robotics
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.
Keywords
Cite
@article{arxiv.2012.11270,
title = {Family Ties: Relating Poncelet 3-Periodics by their Properties},
author = {Ronaldo Garcia and Dan Reznik},
journal= {arXiv preprint arXiv:2012.11270},
year = {2021}
}
Comments
20 pages, 10 figures, 4 tables, 18 video links