OFFSET
0,1
COMMENTS
Average distance between two points chosen at random on two different edges of a unit square.
REFERENCES
Jonathan Borwein, David Bailey, and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery. Natick: A K Peters (2004): p. 66, Example 57(a).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. H. Bailey, J. M. Borwein, V. Kapoor and E. Weisstein, Ten Problems in Experimental Mathematics
Eric Weisstein's World of Mathematics, Square Line Picking
FORMULA
Also equals (2 + sqrt(2) + 5*log(1 + sqrt(2)))/9. - Jean-François Alcover, Feb 14 2014
James D. Klein proved that this constant is equal to 2/3*int(int(sqrt(x^2 + y^2), x = 0..1), y = 0..1) + 1/3*int(int(sqrt(1 + (y - u)^2), u = 0..1), y = 0..1). - John M. Campbell, Apr 02 2016
EXAMPLE
0.86900905527453446388497059434540662485671927963168056966035...
MATHEMATICA
RealDigits[(2 + Sqrt[2] + 5ArcSinh[1])/9, 10, 120][[1]] (* Harvey P. Dale, May 22 2013 *)
PROG
(PARI) (2 + sqrt(2) + 5*asinh(1))/9 \\ G. C. Greubel, Aug 17 2018
(Magma) SetDefaultRealField(RealField(100)); (2 + Sqrt(2) + 5*Argsinh(1))/9; // G. C. Greubel, Aug 17 2018
CROSSREFS
KEYWORD
AUTHOR
Eric W. Weisstein, Jan 16 2004
EXTENSIONS
Broken link fixed by John M. Campbell, Apr 02 2016
STATUS
approved