A195723 Decimal expansion of arctan(golden ratio).

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

Offset

1,4

Comments

The polar angle, in radians, of the cone circumscribed to a regular icosahedron from one of its vertices. - Stanislav Sykora, Feb 15 2014

The angle between the diagonal and the shorter side of a golden rectangle. - Amiram Eldar, May 18 2021

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Index entries for transcendental numbers

Formula

Equals arccos(sqrt((5-sqrt(5))/10)). - Stanislav Sykora, Feb 15 2014

Equals Pi/2 - A195693. - Amiram Eldar, May 18 2021

Example

arctan((1+sqrt(5))/2) = 1.0172219678978513677227...

Mathematica

r=GoldenRatio; N[ArcTan[r], 100]
RealDigits[%] (* A195723 *)

Prog

(PARI) atan((1+sqrt(5))/2) \\ G. C. Greubel, Aug 20 2018
(Magma) SetDefaultRealField(RealField(100)); Arctan((1+Sqrt(5))/2); // G. C. Greubel, Aug 20 2018

Crossrefs

Cf. A001622, A195693, A243445.

Sequence in context: A176704 A289917 A198415 * A138996 A010141 A316247

Adjacent sequences: A195720 A195721 A195722 * A195724 A195725 A195726

Keyword

nonn,cons,easy

Author

Clark Kimberling, Sep 23 2011

Status

approved