9 citations · 19 across the 11 of their papers we have counts for
11 papers · 1 filter
The Wrought Iron Beauty of Poncelet Loci
Dan Reznik
We've built a web-based tool for the real-time interaction with loci of Poncelet triangle families. Our initial goals were to facilitate exploratory detection of geometric properti…
Exploring the Steiner-Soddy Porism
Ronaldo Garcia, Liliana Gheorghe, Dan Reznik
We explore properties and loci of a Poncelet family of polygons -- called here Steiner-Soddy -- whose vertices are centers of circles in the Steiner porism, including conserved qua…
Invariant Center Power and Elliptic Loci of Poncelet Triangles
Mark Helman, Dominique Laurain, Ronaldo Garcia +1
We study center power with respect to circles derived from Poncelet 3-periodics (triangles) in a generic pair of ellipses as well as loci of their triangle centers. We show that (i…
Poncelet Propellers: Invariant Total Blade Area
Dominique Laurain, Daniel Jaud, Dan Reznik
Given a triangle, a trio of circumellipses can be defined, each centered on an excenter. Over the family of Poncelet 3-periodics (triangles) in a concentric ellipse pair (axis-alig…
Family Ties: Relating Poncelet 3-Periodics by their Properties
Ronaldo Garcia, Dan Reznik
We compare loci types and invariants across Poncelet families interscribed in three distinct concentric Ellipse pairs: (i) ellipse-incircle, (ii) circumcircle-inellipse, and (iii)…
Invariants of Self-Intersected N-Periodics in the Elliptic Billiard
Ronaldo Garcia, Dan Reznik
We study self-intersected N-periodics in the elliptic billiard, describing new facts about their geometry (e.g., self-intersected 4-periodics have vertices concyclic with the foci)…