Invariant center power and elliptic loci of Poncelet triangles
type: Item
instance of: scholarly article
title: Invariant center power and elliptic loci of Poncelet triangles
author: Mark Helman
author: Dominique Laurain
author: Dan Reznik
author: Ronaldo A. Garcia
published in: Journal of Dynamical and Control Systems
publication date: 2023-04-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/2102.09438
review text: In this paper the authors studied about the 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. They proved that for any concentric pair, the power of the center with respect to either circumcircle or Euler's circle is invariant, and if a triangle center of a 3-periodic in a generic nested pair is a fixed linear combination of barycenter and circumcenter, its locus over the family is an ellipse. In the last section of the article the authors conclude with three conjectures.
reviewed by: Cătălin Barbu
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 7671520
zbMATH Keywords: porism
zbMATH Keywords: Euclidean
zbMATH Keywords: Poncelet
zbMATH Keywords: locus
zbMATH Keywords: dynamical
zbMATH Keywords: invariant
MaRDI profile type: Publication
OpenAlex ID: W3215509187
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DOI: 10.1007/S10883-021-09580-Z
description: scientific article; zbMATH DE number 7671520