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A091505
Decimal expansion of (2 + sqrt(2) + 5*arcsinh(1))/15.
9
5, 2, 1, 4, 0, 5, 4, 3, 3, 1, 6, 4, 7, 2, 0, 6, 7, 8, 3, 3, 0, 9, 8, 2, 3, 5, 6, 6, 0, 7, 2, 4, 3, 9, 7, 4, 9, 1, 4, 0, 3, 1, 5, 6, 7, 7, 7, 9, 0, 0, 8, 3, 4, 1, 7, 9, 6, 2, 1, 0, 5, 1, 8, 7, 5, 0, 5, 0, 7, 8, 9, 3, 3, 0, 4, 8, 1, 5, 8, 3, 1, 8, 6, 7, 9, 2, 8, 1, 3, 2, 9, 2, 5, 2, 6, 1, 4, 5, 2, 4, 6, 7
OFFSET
0,1
COMMENTS
Or equally, decimal expansion of (2 + sqrt(2) + 5*log(1+sqrt(2)))/15.
Average distance between two points chosen at random in a unit square.
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, Sections 8.1 p. 479 and 8.5 p.498.
L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976, see p. 49.
LINKS
Jens Egholm Pedersen, Jörg Conradt, and Tony Lindeberg, Covariant spatio-temporal receptive fields for neuromorphic computing, arXiv:2405.00318 [cs.NE], 2024. See p. 12.
Eric Weisstein's World of Mathematics, Square Line Picking
EXAMPLE
0.5214054331647206783309823566...
MATHEMATICA
RealDigits[(2+Sqrt[2]+5ArcSinh[1])/15, 10, 120][[1]] (* Harvey P. Dale, Jul 18 2011 *)
PROG
(PARI) (2 + sqrt(2) + 5*asinh(1))/15 \\ G. C. Greubel, Jan 11 2017
CROSSREFS
Sequence in context: A348186 A356030 A266455 * A366626 A030357 A212879
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jan 16 2004
STATUS
approved