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A093524
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Decimal expansion of 3977/216000 - Pi^2/2160.
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3
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0, 1, 3, 8, 4, 2, 7, 7, 5, 7, 4, 0, 2, 3, 6, 4, 0, 8, 0, 4, 6, 8, 3, 5, 8, 8, 3, 7, 9, 6, 3, 5, 3, 6, 3, 3, 7, 3, 3, 6, 5, 1, 0, 6, 5, 0, 8, 9, 2, 4, 0, 3, 7, 4, 7, 0, 9, 9, 9, 3, 8, 1, 9, 7, 3, 3, 2, 3, 1, 4, 6, 0, 7, 3, 0, 3, 6, 1, 4, 7, 9, 0, 5, 4, 1, 6, 5, 8, 4, 5, 6, 4, 6, 4, 2, 6, 5, 9, 6, 1, 8, 8, 9
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OFFSET
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0,3
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COMMENTS
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Average volume of a tetrahedron picked at random in a unit cube.
The exact value of this constant was first calculated by Zinani (2003).
Equals (1/5) times the probability that 5 points independently and uniformly chosen in a cube are the vertices of a re-entrant (concave) polyhedron, i.e., one of the points falls within the tetrahedron formed by the other 4 points. Do and Solomon (1986) evaluated this probability using simulations, and their result is equivalent to an estimate of 0.0139 of this constant, with a 95% confidence interval of [0.01358, 0.01420] (Zinani, 2003). (End)
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LINKS
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EXAMPLE
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0.0138427757...
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MATHEMATICA
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RealDigits[3977/216000-Pi^2/2160, 10, 120][[1]] (* Harvey P. Dale, Oct 31 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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