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
G. C. Greubel, Table of n, a(n) for n = 0..5000
Uwe Bäsel, The moments of the distance between two random points in a regular polygon, arXiv:2101.03815 [math.PR], 2021.
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.
Michael Penn, The average distance between points on a square, video (2022).
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
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jan 16 2004
STATUS
approved