Covering a Sphere with Four Random Circular Caps

2015/02/24 by Steven R. Finch, Finch, Steven R.
Computer Science · Mathematics · #51M04 #51M16 #60D05 (Primary) #62E15 #62H10 #97G60 (Secondary) #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.1502.06931

openalex publication_date 2015/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p(w) denote the probability that four random circular caps of angular radius 70deg84deg; no improvement on the inequality p(w)>=0 for w<84deg is yet feasible. A dual problem involving randomly inscribed well-centered tetrahedra is also examined.

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