24 citations · 112 across the 39 of their papers we have counts for
14 papers · 1 filter
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.
A Web of Confocal Parabolas in a Grid of Hexagons
Peter Moses, Dan Reznik
If one erects regular hexagons upon the sides of a triangle , several surprising properties emerge, including: (i) the triangles which flank said hexagons have an isodynamic poi…
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…
Cramer-Castillon on a Triangle's Incircle and Excircles
Dominique Laurain, Peter Moses, Dan Reznik
The Cramer-Castillon problem (CCP) consists in finding one or more polygons inscribed in a circle such that their sides pass cyclically through a list of points. We study this…
Poncelet Parabola Pirouettes
Dan Reznik, Ronaldo Garcia
We describe some three-dozen curious phenomena manifested by parabolas inscribed or circumscribed about certain Poncelet triangle families. Despite their pirouetting motion, parabo…