Loci of the Brocard Points over Selected Triangle Families

2020/09/18 by Ronaldo Garcia, Garcia, Ronaldo, Dan Reznik +1 · 1 citation
Computer Science · Mathematics · #53A04 and 51M04 and 51N20 #Computational Geometry (cs.CG) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2009.08561

openalex publication_date 2020/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the loci of the Brocard points over two selected families of triangles: (i) 2 vertices fixed on a circumference and a third one which sweeps it, (ii) Poncelet 3-periodics in the homothetic ellipse pair. Loci obtained include circles, ellipses, and teardrop-like curves. We derive expressions for both curves and their areas. We also study the locus of the vertices of Brocard triangles over the homothetic and Brocard-poristic Poncelet families.

Citations

• Related by Similarity II: Poncelet 3-Periodics in the Homothetic Pair and the Brocard Porism

Cited by

• An Infinite, Converging, Sequence of Brocard Porisms

Related

• Family Ties: Relating Poncelet 3-Periodics by their Properties
• Loci of Poncelet Triangles in the General Closure Case
• Harmonious loci of Poncelet triangles about the incircle and their degeneracies
• A Generalization of the Brocard Circle
• Related by Similarity II: Poncelet 3-Periodics in the Homothetic Pair and the Brocard Porism