27 citations · 167 across the 57 of their papers we have counts for
59 papers
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…
Poncelet Spatio-Temporal Surfaces and Tangles
Claudio Esperança, Ronaldo Garcia, Dan Reznik
We explore geometric and topological properties of 3d surfaces swept by Poncelet triangles, as well as tangles formed by associated points.
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…
Triads of Conics Associated with a Triangle
Ronaldo Garcia, Liliana Gheorghe, Peter Moses +1
We revisit constructions based on triads of conics with foci at pairs of vertices of a reference triangle. We find that their 6 vertices lie on well-known conics, whose type we ana…
New Properties and Invariants of Harmonic Polygons
Ronaldo Garcia, Dan Reznik, Pedro Roitman
Via simulation, we discover and prove curious new Euclidean properties and invariants of the Poncelet family of harmonic polygons.
Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family
Filipe Bellio, Ronaldo Garcia, Dan Reznik
We study loci and properties of a Parabola-inscribed family of Poncelet polygons whose caustic is a focus-centered circle. This family is the polar image of a special case of the b…