Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family
arXiv:2111.00979v33 citations
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This work addresses a specialized problem in geometry, focusing on properties of Poncelet polygons, and appears incremental as it builds upon known bicentric families.
The paper investigates a family of Poncelet polygons inscribed in a parabola with a focus-centered circle as caustic, derived from the bicentric family via polar image transformation, and reports findings on closure conditions, loci, and conserved quantities.
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.