%I #27 Nov 17 2022 05:31:10
%S 5,5,0,5,5,2,7,6,8,1,8,8,4,6,9,4,1,5,2,8,2,8,8,3,8,3,2,7,6,4,3,5,5,0,
%T 7,1,8,1,0,3,5,9,7,3,4,4,0,3,2,6,3,4,6,5,3,4,6,2,7,0,3,0,6,2,4,7,6,3,
%U 8,0,7,7,5,0,6,8,6,9,1,9,4,0,2,6,3,8,1,1,9,7,2,4,4,0,2,8,0
%N Decimal expansion of sqrt(16 + 32 / sqrt(5)).
%C The perimeter of a golden rectangle inscribed in a unit circle.
%C The width and height of the rectangle are:
%C W = sqrt(2 - 2 / sqrt(5)) = A179290.
%C H = sqrt(2 + 2 / sqrt(5)) = A121570.
%F Equals (4 / sqrt(5)) * sqrt(5 + 2 * sqrt(5)) = A356869 * A019970.
%F Equals sqrt(5 + 2 * sqrt(5)) / (sqrt(5) / 4) = A019970 / A204188.
%F Equals 4 * sqrt(1 + 2 / sqrt(5)) = 4 * A019952.
%F Equals 4 / sqrt(5 - 2 * sqrt(5)) = 4 / A019934.
%e 5.5055276818846941...
%p sqrt(16 + 32 / sqrt(5));
%t Sqrt[16 + 32/Sqrt[5]]
%o (PARI) sqrt(16 + 32 / sqrt(5))
%Y Cf. A019934, A019952, A019970, A121570, A179290, A204188, A356869.
%K nonn,cons,easy
%O 1,1
%A _Michal Paulovic_, Oct 10 2022