## Ball Triangle Picking

The determination of the probability for obtaining an Obtuse Triangle by picking 3 points at random in the unit Disk was generalized by Hall (1982) to the -D Ball. Buchta (1986) subsequently gave closed form evaluations for Hall's integrals, with the first few solutions being

The case corresponds to the usual Disk case.

Buchta, C. A Note on the Volume of a Random Polytope in a Tetrahedron.'' Ill. J. Math. 30, 653-659, 1986.
Hall, G. R. Acute Triangles in the -Ball.'' J. Appl. Prob. 19, 712-715, 1982.