2021/02/18 by Mark Helman, Helman, Mark, Dominique Laurain +5 · 1 citation
Computer Science · Mathematics · #51M04 #51N20 #51N35 #68T20 #Advanced Mathematical Theories #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Robotics (cs.RO) #cs.GR #cs.RO #math.CV #math.DS #math.MG #msc:51M04 #msc:51N20 #msc:51N35 #msc:68T20
paper · pdf · doi:10.48550/arxiv.2102.09438
25 pages, 16 figures, 6 tables, 8 video links, 7 live app links
openalex publication_date 2021/02/18 · arxiv created 2021/04/16 · arxiv updated 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.