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Poncelet Parabola Pirouettes (2110.06356v5)
Published 12 Oct 2021 in math.MG, cs.CG, and math.DS
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!).