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

Author

Clark Kimberling, Sep 23 2011

Keywords

• nonn
• cons
• easy

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

Examples

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

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2000
• Index entries for transcendental numbers

Crossrefs

Cf. A001622, A195693, A243445.

Programs

Magma

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

Mathematica

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

PARI

atan((1+sqrt(5))/2) \\ G. C. Greubel, Aug 20 2018

Formula

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

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