2010/09/27 by Steven R. Finch, Finch, Steven R., Antonia J. Jones +1 · 1 citation
Physics and Astronomy · #51M25 #60D05 (Primary) 51M04 #62E15 #62H10 #97G60 (Secondary) #FOS: Mathematics #Metric Geometry (math.MG) #Probability (math.PR) #Scientific Research and Discoveries
paper · pdf · doi:10.48550/arxiv.1009.5329
openalex publication_date 2010/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Delta be a random spherical triangle (meaning that vertices are independent and uniform on the unit sphere). A closed-form expression for the area density of Delta has been known since 1867; a complicated integral expression for the perimeter density was found in 1994. Does there exist a closed-form expression for the latter? We attempt to answer this question from several directions. An outcome of our work is the exact value of the perimeter density at the point pi.