9 citations · 19 across the 11 of their papers we have counts for
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Exploring the Dynamics of the Circumcenter Map
Nicholas McDonald, Ronaldo Garcia, Dan Reznik
Using experimental techniques, we study properties of the "circumcenter map", which, upon iterations sends an -gon to a scaled and rotated copy of itself. We also explore th…
New Invariants of Poncelet-Jacobi Bicentric Polygons
Pedro Roitman, Ronaldo Garcia, Dan Reznik
The 1d family of Poncelet polygons interscribed between two circles is known as the Bicentric family. Using elliptic functions and Liouville's theorem, we show (i) that this family…
Average Elliptic Billiard Invariants with Spatial Integrals
Jair Koiller, Dan Reznik, Ronaldo Garcia
We compare invariants of N-periodic trajectories in the elliptic billiard, classic and new, to their aperiodic counterparts via a spatial integrals evaluated over the boundary of t…
A Special Conic Associated with the Reuleaux Negative Pedal Curve
Liliana Gabriela Gheorghe, Dan Reznik
The Negative Pedal Curve of the Reuleaux Triangle w.r. to a point on its boundary consists of two elliptic arcs and a point . Interestingly, the conic passing through the…
The Circumbilliard: Any Triangle can be a 3-Periodic
Dan Reznik, Ronaldo Garcia
A Circumconic passes through a triangle's vertices. We define the Circumbilliard, a circumellipse to a generic triangle for which the latter is a 3-periodic. We study its propertie…