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Properties of Parabola-Inscribed Poncelet Polygons

2021-11-01 14:41:42
Filipe Bellio, Ronaldo Garcia, Dan Reznik
arXiv_RO
 
Abstract

We investigate properties of Poncelet $N$-gon families inscribed in a parabola and circumscribing a focus-centered circle. These can be regarded as the polar images of a bicentric family with respect to the circumcircle, such that the bicentric incircle contains the circumcenter. We derive closure conditions for several $N$ and describe curious Euclidean properties such as straight line, circular, and point, loci, as well as a (perhaps new) conserved quantity.

Abstract (translated)

URL

https://arxiv.org/abs/2111.00979

PDF

https://arxiv.org/pdf/2111.00979.pdf

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