24 citations · 112 across the 39 of their papers we have counts for
17 papers · 1 filter
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)…
The Talented Mr. Inversive Triangle in the Elliptic Billiard
Dan Reznik, Ronaldo Garcia, Mark Helman
Inverting the vertices of elliptic billiard N-periodics with respect to a circle centered on one focus yields a new "focus-inversive" family inscribed in Pascal's Limaçon. The foll…
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)…
An Infinite, Converging, Sequence of Brocard Porisms
Dan Reznik, Ronaldo Garcia
The Brocard porism is a known 1d family of triangles inscribed in a circle and circumscribed about an ellipse. Remarkably, the Brocard angle is invariant and the Brocard points are…
Intriguing Invariants of Centers of Ellipse-Inscribed Triangles
Mark Helman, Ronaldo Garcia, Dan Reznik
We describe invariants of centers of ellipse-inscribed triangle families with two vertices fixed to the ellipse boundary and a third one which sweeps it. We prove that: (i) if a tr…
Loci of the Brocard Points over Selected Triangle Families
Ronaldo Garcia, Dan Reznik
We study the loci of the Brocard points over two selected families of triangles: (i) 2 vertices fixed on a circumference and a third one which sweeps it, (ii) Poncelet 3-periodics…