English

Poncelet Parabola Pirouettes

Metric Geometry 2022-10-11 v5 Computational Geometry Dynamical Systems

Abstract

We describe some three-dozen curious phenomena manifested by parabolas inscribed or circumscribed about certain Poncelet triangle families. Despite their pirouetting motion, parabolas' focus, vertex, directrix, etc., will often sweep or envelop rather elementary loci such as lines, circles, or points. Most phenomena are unproven though supported by solid numerical evidence (proofs are welcome). Some yet unrealized experiments are posed as "challenges" (results are welcome!).

Keywords

Cite

@article{arxiv.2110.06356,
  title  = {Poncelet Parabola Pirouettes},
  author = {Dan Reznik and Ronaldo Garcia},
  journal= {arXiv preprint arXiv:2110.06356},
  year   = {2022}
}

Comments

24 pages, 23 figures

R2 v1 2026-06-24T06:50:35.131Z