A356869 Decimal expansion of 4 / sqrt(5).

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, 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, 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

Offset: 1

Author

Michal Paulovic, Sep 01 2022

Keywords

• nonn
• cons
• easy

Comments

The area of a golden rectangle inscribed in a unit circle.

The width and height of the rectangle are:

W = sqrt(2 - 2 / sqrt(5)) = A179290.

H = sqrt(2 + 2 / sqrt(5)) = A121570.

Examples

			1.7888543819998317...
		

Crossrefs

Cf. A121570, A179290, A204188.

Programs

MATLAB

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

Maple

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

Mathematica

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

Formula

Equals [1; 1, 3, 1, 2] (periodic continued fraction expansion). - Peter Luschny, Sep 02 2022

Equals 1/A204188. - Alois P. Heinz, Sep 02 2022