Original scientific paper

https://doi.org/10.31896/k.25.1

Family Ties: Relating Poncelet 3-Periodics by their Properties

Ronaldo Garcia orcid.org/0000-0001-8876-6956 ; Institute of Mathematics and Statistics of the Federal University of Goiás, Goiás, Brazil
Dan Reznik orcid.org/0000-0002-0542-6014 ; Data Science Consulting, Rio De Janeiro, Brazil

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

invariant; elliptic billiard; locus

Hrčak ID:

269177

URI

https://hrcak.srce.hr/269177

Publication date:

27.12.2021.

Article data in other languages: croatian

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