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Decimal expansion of 4 / sqrt(5).
1

%I #56 Sep 09 2022 23:37:48

%S 1,7,8,8,8,5,4,3,8,1,9,9,9,8,3,1,7,5,7,1,2,7,3,3,8,9,3,4,9,8,5,0,2,0,

%T 9,8,8,3,5,2,4,9,4,6,8,7,6,8,9,2,2,0,5,7,9,4,1,6,7,1,7,7,9,6,3,2,8,4,

%U 1,6,7,4,0,5,1,0,2,4,3,9,1,9,5,3,1,5,3,1,5,2,6,7,0,3,0,2,5

%N Decimal expansion of 4 / sqrt(5).

%C The area 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 [1; 1, 3, 1, 2] (periodic continued fraction expansion). - _Peter Luschny_, Sep 02 2022

%F Equals 1/A204188. - _Alois P. Heinz_, Sep 02 2022

%e 1.7888543819998317...

%p parse(substring(convert(evalf(4 / sqrt(5), 105), string), 1..98));

%t RealDigits[4 / Sqrt[5], 10, 105][[1]][[Range[1, 97]]]

%o (MATLAB) cell2mat(struct2cell(struct(vpa(4 / sqrt(5), 105)))); ans(1:98)

%Y Cf. A121570, A179290, A204188.

%K nonn,cons,easy

%O 1,2

%A _Michal Paulovic_, Sep 01 2022