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A348669 Decimal expansion of 2*sqrt(2)*log(1 + sqrt(2))/(3*Pi). 0
2, 6, 4, 5, 0, 5, 0, 0, 7, 0, 0, 7, 8, 6, 9, 8, 4, 5, 5, 1, 5, 7, 7, 5, 2, 0, 1, 2, 9, 7, 2, 2, 5, 2, 6, 9, 3, 6, 3, 4, 0, 0, 0, 9, 0, 9, 6, 8, 0, 5, 1, 8, 3, 0, 5, 6, 2, 2, 4, 4, 3, 7, 2, 5, 8, 6, 4, 0, 2, 1, 3, 7, 3, 7, 6, 4, 3, 5, 6, 7, 9, 4, 6, 7, 5, 8, 9, 8, 3, 5, 6, 9, 7, 2, 3, 5, 1, 3, 7, 2, 5, 3, 4, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
The average length of a random line segment in a unit square defined as follows. A line that is making a random angle with a given edge of the square is chosen, and a random distance of this line from a given vertex of this edge is chosen uniformly between 0 and the distance to the opposite vertex in the square. The segment is then being chosen by picking at random two points between the two intersection points of the line with the perimeter of the square.
LINKS
Eric Rosenberg, The expected length of a random line segment in a rectangle, Operations Research Letters, Vol. 32, No. 2 (2004), pp. 99-102.
EXAMPLE
0.26450500700786984551577520129722526936340009096805...
MAPLE
evalf(sqrt(8/9)*arcsinh(1)/Pi, 120); # Alois P. Heinz, Oct 29 2021
MATHEMATICA
RealDigits[2*Sqrt[2]*Log[1 + Sqrt[2]]/(3*Pi), 10, 100][[1]]
PROG
(PARI) 2*sqrt(2)*log(1 + sqrt(2))/(3*Pi) \\ Michel Marcus, Oct 29 2021
CROSSREFS
Sequence in context: A057143 A087428 A115508 * A195730 A222236 A351001
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Oct 29 2021
STATUS
approved

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Last modified July 23 21:46 EDT 2024. Contains 374575 sequences. (Running on oeis4.)