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%I #16 Aug 21 2023 12:31:11
%S 5,6,3,4,6,5,1,1,3,6,8,2,8,5,9,3,9,5,4,2,2,8,3,5,8,3,0,6,9,3,2,3,3,7,
%T 9,8,0,7,1,5,5,5,7,9,7,9,4,6,5,3,3,7,4,3,6,6,2,1,6,0,6,1,2,1,7,5,6,9,
%U 7,5,9,7,0,3,8,0,5,8,3,3,6,2,4,6,9,3,5,2,3,6,9,0,3,7,7,3,0,9,9,9,3,5,9,8,8
%N Decimal expansion of the edge length of a regular 11-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 = 11, and the constant, a = e(11), 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="/A272489/b272489.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_10">Index entries for algebraic numbers, degree 10</a>
%F Equals 2*sin(Pi/11) = 2*cos(Pi*9/22).
%e 0.5634651136828593954228358306932337980715557979465337436621606121...
%t RealDigits[N[2Sin[Pi/11], 100]][[1]] (* _Robert Price_, May 01 2016 *)
%o (PARI) 2*sin(Pi/11)
%Y Cf. A004169, A019434.
%Y Edge lengths of nonconstructible n-gons: A272487 (n=7), A272488 (n=9), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19).
%K nonn,cons,easy
%O 0,1
%A _Stanislav Sykora_, May 01 2016
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