A357715 Decimal expansion of sqrt(16 + 32 / sqrt(5)).

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, 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, 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

Offset: 1

Author

Michal Paulovic, Oct 10 2022

Keywords

• nonn
• cons
• easy

Comments

The perimeter 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

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Crossrefs

Cf. A019934, A019952, A019970, A121570, A179290, A204188, A356869.

Programs

Maple

sqrt(16 + 32 / sqrt(5));

Mathematica

Sqrt[16 + 32/Sqrt[5]]

PARI

sqrt(16 + 32 / sqrt(5))

Formula

Equals (4 / sqrt(5)) * sqrt(5 + 2 * sqrt(5)) = A356869 * A019970.

Equals sqrt(5 + 2 * sqrt(5)) / (sqrt(5) / 4) = A019970 / A204188.

Equals 4 * sqrt(1 + 2 / sqrt(5)) = 4 * A019952.

Equals 4 / sqrt(5 - 2 * sqrt(5)) = 4 / A019934.