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A348683
Decimal expansion of the average length of a chord in a unit cube defined by the intersection of the surface with a straight line passing through 2 points uniformly and independently chosen at random in the interior of the cube.
4
1, 1, 0, 2, 8, 4, 5, 3, 0, 3, 7, 7, 8, 6, 2, 7, 0, 5, 8, 5, 9, 3, 0, 5, 1, 8, 8, 8, 7, 4, 7, 3, 5, 5, 9, 6, 9, 5, 7, 7, 3, 3, 3, 5, 5, 9, 6, 5, 1, 5, 8, 9, 3, 4, 1, 3, 4, 8, 2, 4, 0, 3, 8, 2, 4, 6, 5, 9, 7, 4, 4, 1, 0, 2, 3, 0, 9, 9, 6, 0, 5, 2, 1, 7, 7, 7, 5, 4, 1, 3, 4, 6, 1, 3, 5, 1, 1, 8, 6, 6, 9, 1, 9, 5, 1
OFFSET
1,4
LINKS
Rodney Coleman, Random paths through convex bodies, Journal of Applied Probability, Vol. 6, No. 2 (1969), pp. 430-441; alternative link; author's link.
FORMULA
Equals 4/63 - Pi/9 + 17*sqrt(2)/63 - 2*sqrt(3)/21 + log(1+sqrt(2))/3 + 2*log(2+sqrt(3))/3.
EXAMPLE
1.10284530377862705859305188874735596957733355965158...
MATHEMATICA
RealDigits[4/63 - Pi/9 + 17*Sqrt[2]/63 - 2*Sqrt[3]/21 + Log[1+Sqrt[2]]/3 + 2*Log[2+Sqrt[3]]/3, 10, 100][[1]]
PROG
(PARI) 4/63 - Pi/9 + 17*sqrt(2)/63 - 2*sqrt(3)/21 + log(1+sqrt(2))/3 + 2*log(2+sqrt(3))/3 \\ Michel Marcus, Oct 29 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Oct 29 2021
STATUS
approved