cp's OEIS Frontend

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

%I A130880 #55 Mar 16 2025 10:43:24
%S A130880 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,
%T A130880 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,
%U A130880 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
%N A130880 Decimal expansion of 2*sin(Pi/18).
%C A130880 Also: a bond percolation threshold probability on the triangular lattice.
%C A130880 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
%D A130880 John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 207.
%D A130880 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.18.1, p. 373.
%H A130880 Stanislav Sykora, <a href="/A130880/b130880.txt">Table of n, a(n) for n = 0..2000</a>
%H A130880 Steven R. Finch, <a href="http://dx.doi.org/10.1007/BF01608791">Several Constants Arising in Statistical Mechanics</a>, Annals Combinat., Vol. 3, Issue 2-4 (1999), pp. 323-335.
%H A130880 Wikipedia, <a href="http://en.wikipedia.org/wiki/Constructible_number">Constructible number</a>.
%H A130880 Wikipedia, <a href="https://en.wikipedia.org/wiki/Percolation_threshold">Percolation threshold</a>.
%H A130880 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a>.
%H A130880 <a href="/index/Al#algebraic_03">Index entries for algebraic numbers, degree 3</a>.
%F A130880 Equals 2*A019819 = A019829/A019889.
%F A130880 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
%F A130880 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
%F A130880 Equals -1 + Product_{k>=3} (1 - (-1)^k/A063289(k)). - _Amiram Eldar_, Nov 22 2024
%F A130880 Equals A133749/2 = 1 - A178959. - _Hugo Pfoertner_, Dec 15 2024
%e A130880 0.347296355333860697703433253538629592...
%t A130880 RealDigits[N[2Sin[Pi/18], 100]][[1]] (* _Robert Price_, May 01 2016 *)
%o A130880 (PARI) 2*sin(Pi/18)
%Y A130880 Cf. A004169, A019819, A019829, A019889, A063289, A133749, A178959, A332437, A332438.
%Y A130880 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
%K A130880 cons,nonn
%O A130880 0,1
%A A130880 _R. J. Mathar_, Jul 26 2007