2025/02/06 by Norbert Hungerbühler, Hungerbühler, Norbert, Micha Wasem +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2502.04017
openalex publication_date 2025/02/06 · openalex created_date 2025/02/08 · openalex updated_date 2026/07/28
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.