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arXiv · 2106.00715

Poncelet Triangles: a Theory for Locus Ellipticity

Mark Helman·Dominique Laurain·Dan Reznik·Ronaldo Garcia
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Abstract

We present a theory which predicts if the locus of a triangle center over certain Poncelet triangle families is a conic or not. We consider families interscribed in (i) the confocal pair and (ii) an outer ellipse and an inner concentric circular caustic. Previously, determining if a locus was a conic was done on a case-by-case basis. In the confocal case, we also derive conditions under which a locus degenerates to a segment or a circle. We show the locus' turning number is +/- 3, while predicting its monotonicity with respect to the motion of a vertex of the triangle family.

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BibTeXRIS

Mark Helman, Dominique Laurain, Dan Reznik, Ronaldo Garcia. 2021-06-01. Poncelet Triangles: a Theory for Locus Ellipticity. https://arxiv.org/abs/2106.00715

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