A130880 Decimal expansion of 2*sin(Pi/18).

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

Offset

0,1

Comments

Also: a bond percolation threshold probability on the triangular lattice.

Also: the edge length of a regular 18-gon with unit circumradius. Such an m-gon is not constructible using a compass and a straightedge (see A004169). With an even m, in fact, it would be constructible only if the (m/2)-gon were constructible, which is not true in this case (see A272488). - Stanislav Sykora, May 01 2016

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.18.1, p. 373.

Links

Stanislav Sykora, Table of n, a(n) for n = 0..2000

Steven R. Finch, Several Constants Arising in Statistical Mechanics, Annals Combinat., Vol. 3, Issue 2-4 (1999), pp. 323-335.

Wikipedia, Constructible number.

Wikipedia, Percolation threshold.

Wikipedia, Regular polygon.

Index entries for algebraic numbers, degree 3.

Formula

Equals 2*A019819 = A019829/A019889.

Algebraic number with minimal polynomial over Q equal to x^3 - 3*x + 1, a cyclic cubic, having zeros 2*sin(Pi/18) (= 2*cos(4*Pi/9)), 2*sin(5*Pi/18) (= 2*cos(2*Pi/9)) and -2*sin(7*Pi/18) (= -2*cos(Pi/9)). Cf. A332437. - Peter Bala, Oct 23 2021

Equals 2 + rho(9) - rho(9)^2, an element of the extension field Q(rho(9)), with rho(9) = 2*cos(Pi/9) = A332437 with minimal polynomial x^3 - 3*x - 1 over Q. - Wolfdieter Lang, Sep 20 2022

Equals -1 + Product_{k>=3} (1 - (-1)^k/A063289(k)). - Amiram Eldar, Nov 22 2024

Equals A133749/2 = 1 - A178959. - Hugo Pfoertner, Dec 15 2024

Example

0.347296355333860697703433253538629592...

Mathematica

RealDigits[N[2Sin[Pi/18], 100]][[1]] (* Robert Price, May 01 2016 *)

Prog

(PARI) 2*sin(Pi/18)

Crossrefs

Cf. A004169, A019819, A019829, A019889, A063289, A133749, A178959, A332437, A332438.

Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A272491 (n=19). - Stanislav Sykora, May 01 2016

Sequence in context: A230159 A105828 A209873 * A026248 A082089 A089961

Adjacent sequences: A130877 A130878 A130879 * A130881 A130882 A130883

Keyword

cons,nonn

Author

R. J. Mathar, Jul 26 2007

Status

approved