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A355186
Decimal expansion of 2*log(sqrt(2)+1)/Pi.
1
5, 6, 1, 0, 9, 9, 8, 5, 2, 3, 3, 9, 1, 8, 0, 1, 2, 7, 1, 3, 5, 7, 1, 9, 5, 8, 8, 9, 3, 5, 2, 3, 9, 6, 9, 2, 8, 0, 8, 8, 7, 2, 4, 2, 4, 6, 2, 8, 0, 9, 9, 9, 2, 5, 8, 9, 9, 5, 5, 9, 3, 1, 2, 6, 7, 0, 5, 5, 5, 8, 5, 5, 7, 8, 8, 0, 5, 6, 3, 6, 3, 0, 5, 3, 9, 4, 5, 3, 8, 8, 1, 1, 6, 0, 7, 0, 0, 8, 2, 9, 2, 3, 0, 2, 7
OFFSET
0,1
COMMENTS
The average distance between the center of a unit square to a point on its perimeter uniformly chosen by a random direction from the center.
If the point is uniformly chosen at random on the perimeter, then the average is (sqrt(2) + arcsinh(1))/4 (A345653).
LINKS
Mark Dalthorp, Escape the Square, Mathematics Magazine, Vol. 87, No. 1 (2014), p. 68.
FORMULA
Equals arcsinh(1)/arcsin(1).
EXAMPLE
0.56109985233918012713571958893523969280887242462809...
MATHEMATICA
RealDigits[2*ArcSinh[1]/Pi, 10, 100][[1]]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 23 2022
STATUS
approved