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Cube Triangle Picking

Pick 3 points at random in the unit $n$-Hypercube. Denote the probability that the three points form an Obtuse Triangle $\Pi(n)$. Langford (1969) proved

\Pi(2)={\textstyle{97\over 150}}+{\textstyle{1\over 40}}\pi=0.725206483\ldots.

See also Ball Triangle Picking, Cube Point Picking


Finch, S. ``Favorite Mathematical Constants.''

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.

© 1996-9 Eric W. Weisstein