2021/10/12 by Dan Reznik, Reznik, Dan, Garcia, Ronaldo
Mathematics · #51M04 #51N20 #51N35 #68T20 #Computational Geometry (cs.CG) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2110.06356
openalex publication_date 2021/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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!).