The stationary focus of the Kiepert parabola over a special Poncelet triangle family

2025/12/18 by Helman, Mark, Garcia, Ronaldo A., Reznik, Dan
Mathematics · Physics and Astronomy · #Mathematics and Applications #Algebraic and Geometric Analysis #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2512.16678

Abstract

We show that the focus of the Kiepert in-parabola remains stationary over a family of circle-inscribed Poncelet triangles which contain an equilateral triangle.

Citations

• Harmonious loci of Poncelet triangles about the incircle and their degeneracies
• New Properties of Triangular Orbits in Elliptic Billiards
• Billiards in ellipses revisited
• On the circumcenters of triangular orbits in elliptic billards

Related

• Parable of the Parabola
• Four special Poncelet triangle families about the incircle
• Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family
• Poncelet Parabola Pirouettes
• Poncelet pairs of a circle and parabolas from a confocal family and Painlevé VI equations