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