Four special Poncelet triangle families about the incircle

2025/12/19 by Ronaldo A. Garcia, Garcia, Ronaldo A., Mark Helman +3
Mathematics · #51M04 #51N20 #51N35 #68T20 #Algebraic and Geometric Analysis #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2512.17440

openalex publication_date 2025/12/19 · openalex created_date 2025/12/23 · openalex updated_date 2026/07/28

Abstract

We describe four special families of ellipse-inscribed Poncelet triangles about the incircle which maintain certain triangle centers stationary and which also display interesting conservations.

Citations

• Harmonious loci of Poncelet triangles about the incircle and their degeneracies
• Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family
• Family Ties: Relating Poncelet 3-Periodics by their Properties

Related

• Harmonious loci of Poncelet triangles about the incircle and their degeneracies
• Family Ties: Relating Poncelet 3-Periodics by their Properties
• Loci of Poncelet Triangles in the General Closure Case
• Invariant Center Power and Elliptic Loci of Poncelet Triangles
• Parabola-Inscribed Poncelet Polygons Derived from the Bicentric Family