Pick 3 points at random in the unit -Hypercube. Denote the probability that the three points form an
Obtuse Triangle . Langford (1969) proved
See also Ball Triangle Picking, Cube Point Picking
References
Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/geom/geom.html
Langford, E. ``The Probability that a Random Triangle is Obtuse.'' Biometrika 56, 689-690, 1969.
Santaló, L. A. Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley, 1976.