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A093591
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Decimal expansion of (12*Pi)/715.
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4
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0, 5, 2, 7, 2, 6, 0, 3, 0, 5, 4, 9, 7, 5, 8, 7, 6, 7, 6, 3, 8, 5, 3, 3, 8, 7, 4, 9, 6, 4, 1, 3, 1, 5, 1, 6, 9, 3, 7, 5, 7, 4, 8, 7, 1, 0, 3, 8, 4, 6, 3, 3, 1, 4, 4, 7, 7, 9, 0, 1, 1, 6, 7, 9, 8, 2, 7, 8, 8, 5, 2, 7, 0, 9, 8, 5, 0, 9, 8, 0, 1, 3, 7, 5, 5, 7, 5, 4, 0, 9, 6, 5, 6, 0, 9, 1, 4, 7, 5, 2, 6, 6, 8
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OFFSET
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0,2
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COMMENTS
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Mean volume of a tetrahedron formed by four random points in a unit ball.
Equals (4*Pi/15) times the probability (9/143) that 5 points independently and uniformly chosen in a ball 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. It was calculated by the Czech physicist and mathematician Bohuslav Hostinský (1884 - 1951) in 1925. - Amiram Eldar, Aug 25 2020
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REFERENCES
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Bohuslav Hostinský, Sur les probabilités géométriques, Brno: Publications de la Faculté des sciences de l'Université Masaryk, 1925.
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LINKS
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EXAMPLE
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0.0527260305...
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MATHEMATICA
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RealDigits[12*Pi/715, 10, 100][[1]] (* Amiram Eldar, Aug 25 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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