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Loci of Poncelet Triangles with Multiple Caustics

2021-08-11 20:04:41
Ronaldo Garcia, Boris Odehnal, Dan Reznik
arXiv_RO
 
Abstract

We analyze loci of triangles centers over variants of two-well known triangle porisms: the bicentric family and the confocal family. Specifically, we evoke a more general version of Poncelet's closure theorem whereby individual sides can be made tangent to separate caustics. We show that despite a more complicated dynamic geometry, the locus of certain triangle centers and associated points remain conics and/or circles.

Abstract (translated)

URL

https://arxiv.org/abs/2108.05430

PDF

https://arxiv.org/pdf/2108.05430.pdf

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