Poncelet Curves
Differential Geometry
2025-09-15 v2 Dynamical Systems
Abstract
We examine pairs of closed plane curves that have the same closing property as two conic sections in Poncelet's porism. We show how the vertex curve can be computed for a given envelope and vice versa. Our formulas are universal in the sense that they produce all possible sufficiently regular pairs of such Poncelet curves. We arrive at similar results for sets of curves, analogous to the pencil of conic sections in the full Poncelet theorem. We also study the case of Poncelet curves that carry Poncelet polygons which are equiangular or even congruent.
Cite
@article{arxiv.2502.04017,
title = {Poncelet Curves},
author = {Norbert Hungerbühler and Micha Wasem},
journal= {arXiv preprint arXiv:2502.04017},
year = {2025}
}
Comments
21 pages, 10 figures, final version to appear in ZAMM - Journal of Applied Mathematics and Mechanics