OFFSET
1,3
COMMENTS
The average length of chords in a unit square drawn between two points uniformly and independently chosen at random on two opposite sides. - Amiram Eldar, Aug 08 2020
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
D. H. Bailey and J. M. Borwein, Highly Parallel, High-Precision Numerical Integration, Lawrence Berkeley National Laboratory (2005), p. 9.
Philip W. Kuchel and Rodney J. Vaughan, Average lengths of chords in a square, Mathematics Magazine, Vol. 54, No. 5 (1981), pp. 261-269.
FORMULA
EXAMPLE
1.076635732895178008965379750243226282838269703135986...
MATHEMATICA
RealDigits[2/3 - Sqrt[2]/3 + ArcSinh[1], 10, 103] // First
PROG
(PARI) default(realprecision, 100); (2 + sqrt(2) + 5*log(1+sqrt(2)))/3 \\ G. C. Greubel, Aug 31 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (2 + Sqrt(2) + 5*Log(1+Sqrt(2)))/3; // G. C. Greubel, Aug 31 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Sep 22 2014
STATUS
approved