2010/12/03 by Steven R. Finch, Finch, Steven R.
Mathematics · #33C05 #33E05 (Secondary) #51M25 #60D05 (Primary) 51M04 #62E15 #62H10 #97G60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Point processes and geometric inequalities #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1012.0781
openalex publication_date 2010/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let alpha be an arbitrary angle in a random spherical triangle Delta and a be the side opposite alpha. (The sphere has radius 1; vertices of Delta are independent and uniform.) If some other side is constrained to be pi/2, then E(alpha*a)=3.05.... If instead some other angle is fixed at pi/2, then E(alpha*a)=2.87.... In our study of the latter scenario, both Apery's constant and Catalan's constant emerge. We also review Miles' 1971 proof that E(alpha*a)=pi2/2-2 when no constraints are in place.