arXiv:2102.09438
Invariant Center Power and Elliptic Loci of Poncelet Triangles
Invariant Center Power and Elliptic Loci of Poncelet Triangles
著者: Mark Helman, Dominique Laurain, Ronaldo Garcia, Dan Reznik
分類: math.MG, cs.GR, cs.RO, math.CV, math.DS
原文アブストラクト
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) for any concentric pair, the power of the center with respect to either circumcircle or Euler's circle is invariant, and (ii) if a triangle center of a 3-periodic in a generic nested pair is a fixed affine combination of barycenter and circumcenter, its locus over the family is an ellipse.