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A093525
Decimal expansion of 13/720 - Pi^2/15015.
1
0, 1, 7, 3, 9, 8, 2, 3, 9, 2, 4, 5, 1, 2, 6, 6, 9, 3, 8, 4, 2, 6, 7, 9, 4, 6, 5, 5, 7, 8, 8, 7, 3, 8, 2, 7, 2, 0, 8, 2, 1, 5, 3, 1, 5, 8, 3, 4, 7, 9, 3, 5, 9, 8, 1, 3, 7, 8, 7, 9, 0, 0, 8, 8, 1, 0, 5, 5, 2, 5, 5, 5, 5, 6, 7, 3, 8, 2, 4, 4, 8, 3, 1, 3, 2, 6, 4, 3, 9, 5, 1, 5, 5, 7, 0, 7, 5, 0, 0, 1, 2, 8, 8
OFFSET
0,3
COMMENTS
Average volume of a tetrahedron picked at random in a tetrahedron with unit volume.
Buchta & Reitzner announced this result in 1992, and Mannion (independently) proved it in 1994. Buchta & Reitzner proved a more general result in 2001. - Charles R Greathouse IV, Sep 04 2015
Klee (1969) conjectured that the average volume is 1/60 and stated that according to Monte Carlo experiments 1/57 is the integer-reciprocal closest to this value. - Amiram Eldar, Apr 09 2022
EXAMPLE
0.0173982392...
MATHEMATICA
Join[{0}, RealDigits[13/720 - Pi^2/15015, 10, 100][[1]]] (* Amiram Eldar, Apr 09 2022 *)
PROG
(PARI) 13/720 - Pi^2/15015 \\ Charles R Greathouse IV, Sep 04 2015
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Mar 30 2004
EXTENSIONS
Added initial 0 to make offset correct. - N. J. A. Sloane, Feb 08 2015
STATUS
approved