Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family
Filipe Bellio, Ronaldo Garcia, Dan Reznik
TL;DR
This paper explores a special family of Poncelet polygons inscribed in a parabola, focusing on their geometric properties, loci, and conserved quantities, linked to bicentric polygons through polar transformations.
Contribution
It introduces a novel parabola-inscribed Poncelet polygon family derived from bicentric polygons, detailing their closure conditions and geometric invariants.
Findings
Identification of loci and properties of the parabola-inscribed Poncelet polygons
Derivation of closure conditions and conserved quantities
Connection between parabola-inscribed and bicentric polygons via polar image
Abstract
We study loci and properties of a Parabola-inscribed family of Poncelet polygons whose caustic is a focus-centered circle. This family is the polar image of a special case of the bicentric family with respect to its circumcircle. We describe closure conditions, curious loci, and new conserved quantities.
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Taxonomy
TopicsMathematics and Applications · Advanced Theoretical and Applied Studies in Material Sciences and Geometry · Advanced Mathematical Theories and Applications