A272491 - OEIS

%I #15 Aug 21 2023 12:31:09

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

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

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

%N Decimal expansion of the edge length of a regular 19-gon with unit circumradius.

%C The edge length e(m) of a regular m-gon is e(m) = 2*sin(Pi/m). In this case, m = 19, and the constant, a = e(19), is not constructible using a compass and a straightedge (see A004169). With an odd m, in fact, e(m) would be constructible only if m were a Fermat prime (A019434).

%H Stanislav Sykora, <a href="/A272491/b272491.txt">Table of n, a(n) for n = 0..2000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Constructible_number">Constructible number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a>

%H <a href="/index/Al#algebraic_18">Index entries for algebraic numbers, degree 18</a>

%F Equals 2*sin(Pi/19) = 2*cos(Pi*17/38).

%e 0.32918918056146778828730411817587683902434496671930824670294254...

%t RealDigits[N[2Sin[Pi/19], 100]][[1]] (* _Robert Price_, May 01 2016 *)

%o (PARI) 2*sin(Pi/19)

%Y Cf. A004169, A019434.

%Y Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18).

%K nonn,cons,easy

%O 0,1

%A _Stanislav Sykora_, May 01 2016