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
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
S. R. Finch, Several Constants Arising in Statistical Mechanics, Annals Combinat. vol 3 (1999) issue (2-4) pp. 323-335.
Wikipedia, Constructible number
Wikipedia, Percolation threshold
Wikipedia, Regular polygon
FORMULA
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
EXAMPLE
0.34729635533386069770....
MATHEMATICA
RealDigits[N[2Sin[Pi/18], 100]][[1]] (* Robert Price, May 01 2016 *)
PROG
(PARI) 2*sin(Pi/18)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, Jul 26 2007
STATUS
approved