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

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.