Cycling along Euler road

2025/08/04 by Dylan Wyrzykowski, Wyrzykowski, Dylan · 1 citation
Mathematics · #51M04 #51N20 #Advanced Combinatorial Mathematics #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary 51M05

paper · pdf · doi:10.48550/arxiv.2509.10460

openalex publication_date 2025/08/04 · openalex created_date 2025/10/12 · openalex updated_date 2026/08/01

Abstract

We introduce the notion of P_λ points, which canonically parametrize points on the Euler line. This allows us to show that the Euler line of any d-dimensional inscribed polygon in Euclidean space arises from the Euler lines of its sub-polygons, beginning from the Euler line of a point in the plane. Furthermore, we situate P_λ points in the literature of modern triangle centers.

Citations

• More Relationships between a Central Quadrilateral and its Reference Quadrilateral

Cited by

• A Family of Eight-Point Conics Associated with the Cyclic Quadrilateral

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