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A093524 Decimal expansion of 3977/216000 - Pi^2/2160. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Average volume of a tetrahedron picked at random in a unit cube.
From Amiram Eldar, Aug 25 2020: (Start)
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)
LINKS
Kim-Anh Do and Herbert Solomon, A simulation study of Sylvester's problem in three dimensions, Journal of applied probability, Vol. 23, No. 2 (1986), pp. 509-513, alternative link.
Eric Weisstein's World of Mathematics, Cube Tetrahedron Picking.
Alessandro Zinani, The expected volume of a tetrahedron whose vertices are chosen at random in the interior of a cube, Monatshefte für Mathematik, Vol. 139, No. 4 (2003), pp. 341-348.
EXAMPLE
0.0138427757...
MATHEMATICA
RealDigits[3977/216000-Pi^2/2160, 10, 120][[1]] (* Harvey P. Dale, Oct 31 2013 *)
CROSSREFS
Cf. A093591.
Sequence in context: A086179 A185453 A021967 * A200343 A199456 A242030
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Mar 30 2004
EXTENSIONS
Added initial 0 to match offset. - N. J. A. Sloane, Feb 08 2015
STATUS
approved

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Last modified March 19 07:41 EDT 2024. Contains 370958 sequences. (Running on oeis4.)