A019916 Decimal expansion of tan(Pi/10) (angle of 18 degrees).

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

In a regular pentagon inscribed in a unit circle this is the cube of the length of the side divided by 5: (1/5)*(sqrt(3 - phi))^3 with phi from A001622. - Wolfdieter Lang, Jan 08 2018

Quartic number of denominator 5 and minimal polynomial 5x^4 - 10x^2 + 1. - Charles R Greathouse IV, May 13 2019

Examples

			0.3249196962329063261558714122151344649549034715214751003078047191...
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Wikipedia, Exact trigonometric constants
• Index entries for algebraic numbers, degree 4.

Crossrefs

Cf. A001622, A019827 (sin(Pi/10)), A019881 (cos(Pi/10)).

Programs

Mathematica

RealDigits[Tan[18 Degree],10,120][[1]] (* Harvey P. Dale, Mar 07 2012 *)

PARI

tan(Pi/10) \\ Michel Marcus, Jan 08 2018

PARI

polrootsreal(5*x^4-10*x^2+1)[3] \\ Charles R Greathouse IV, Feb 04 2025

Formula

Equals A019827/A019881 = 1/A019970 = 1/sqrt(5+2*sqrt(5)). - R. J. Mathar, Jul 26 2010

Equals tan((phi - 1)/sqrt(2 + phi)) = (1/5)*(sqrt(3 - phi))^3 = (3 - phi)*sqrt(3 - phi)/5 = sqrt(7 - 4*phi)/(2*phi - 1), with phi from A001622. - Wolfdieter Lang, Jan 08 2018

Equals Product_{k>=0} ((5*k + 1)/(5*k + 4))^(-1)^(k) = Product_{k>=0} A090771(k)/A090773(k). - Antonio Graciá Llorente, Mar 24 2024