9 citations · 16 across the 4 of their papers we have counts for
4 papers
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…
Related by Similarity II: Poncelet 3-Periodics in the Homothetic Pair and the Brocard Porism
Dan Reznik, Ronaldo Garcia
Previously we showed the family of 3-periodics in the elliptic billiard (confocal pair) is the image under a variable similarity transform of poristic triangles (those with non-con…
Area-Invariant Pedal-Like Curves Derived from the Ellipse
Dan Reznik, Ronaldo Garcia, Hellmuth Stachel
We study six pedal-like curves associated with the ellipse which are area-invariant for pedal points lying on one of two shapes: (i) a circle concentric with the ellipse, or (ii) t…
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…