5 papers · 1 filter
Fregier Ellipses
Dominique Laurain
We introduce Fregier ellipses which generalize the Fregier point in euclidean geometry. Subject is related to Dynamical Systems and Poncelet's closure theorem aka Poncelet porism a…
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 Triangles: a Theory for Locus Ellipticity
Mark Helman, Dominique Laurain, Dan Reznik +1
We present a theory which predicts if the locus of a triangle center over certain Poncelet triangle families is a conic or not. We consider families interscribed in (i) the confoca…
Invariant Center Power and Elliptic Loci of Poncelet Triangles
Mark Helman, Dominique Laurain, Ronaldo Garcia +1
We study center power with respect to circles derived from Poncelet 3-periodics (triangles) in a generic pair of ellipses as well as loci of their triangle centers. We show that (i…
Poncelet Propellers: Invariant Total Blade Area
Dominique Laurain, Daniel Jaud, Dan Reznik
Given a triangle, a trio of circumellipses can be defined, each centered on an excenter. Over the family of Poncelet 3-periodics (triangles) in a concentric ellipse pair (axis-alig…