Triangles Formed via Poisson Nearest Neighbors

2017/12/21 by Steven R. Finch, Finch, Steven R.
Computer Science · Mathematics · #51M04 #51M25 #52A22 #52A38 (Secondary) #60D05 (Primary) 60G55 #62E15 #62H10 #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1712.08481

openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We start with certain joint densities (for sides and for angles) corresponding to pinned Poissonian triangles in the plane, then discuss analogous results for staked and anchored triangles.

Citations

• Random Gaussian Tetrahedra
• Rank-3 Projections of a 4-Cube
• Pins, Stakes, Anchors and Gaussian Triangles

Related

• 0-Pierced Triangles within a Poisson Overlay
• Pins, Stakes, Anchors and Gaussian Triangles
• Uniform Triangles with Equality Constraints
• Heat content determines planar triangles
• The proportion of triangles in a class of anisotropic Poisson line tessellations