Ball triangle picking is the selection of triples of points (corresponding to vertices of a general triangle) randomly placed inside a ball. n random triangles can be picked in a unit ball in the Wolfram Language using the function RandomPoint[Ball[], {n, 3}]. The distribution of areas of a triangle with vertices picked at random in a unit ball is illustrated above. The mean triangle area is A^_ = 9/77 π (Buchta and Müller 1984, Finch 2010).
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