A355186 - OEIS

%I #6 Jun 23 2022 13:49:35

%S 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,

%T 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,

%U 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

%N Decimal expansion of 2*log(sqrt(2)+1)/Pi.

%C 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.

%C If the point is uniformly chosen at random on the perimeter, then the average is (sqrt(2) + arcsinh(1))/4 (A345653).

%H Mark Dalthorp, <a href="http://www.jstor.org/stable/10.4169/math.mag.87.1.61">Escape the Square</a>, Mathematics Magazine, Vol. 87, No. 1 (2014), p. 68.

%F Equals arcsinh(1)/arcsin(1).

%F Equals A060294 * A091648 = A091648 / A019669.

%e 0.56109985233918012713571958893523969280887242462809...

%t RealDigits[2*ArcSinh[1]/Pi, 10, 100][[1]]

%Y Cf. A019669, A060294, A091648, A345653.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Jun 23 2022