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arXiv · 2110.06356

Poncelet Parabola Pirouettes

Dan Reznik·Ronaldo Garcia
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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!).

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Dan Reznik, Ronaldo Garcia. 2021-10-12. Poncelet Parabola Pirouettes. https://arxiv.org/abs/2110.06356

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