English

Fregier Ellipses

Metric Geometry 2022-06-09 v1 Dynamical Systems

Abstract

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 and displaying geometric invariants (area,angles). Special angles pi/3 and 2pi/3 are emphasized and we show that we have invariant sum of areas for Fregier circles in general Poncelet configuration, occuring from an affine map of the elliptical billiard.

Keywords

Cite

@article{arxiv.2206.03747,
  title  = {Fregier Ellipses},
  author = {Dominique Laurain},
  journal= {arXiv preprint arXiv:2206.03747},
  year   = {2022}
}

Comments

7 pages, 4 figures

R2 v1 2026-06-24T11:43:11.242Z