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Decimal expansion of sqrt(16 + 32 / sqrt(5)).
0

%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