This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A272488 #25 Aug 29 2025 13:55:31 %S A272488 6,8,4,0,4,0,2,8,6,6,5,1,3,3,7,4,6,6,0,8,8,1,9,9,2,2,9,3,6,4,5,1,9,1, %T A272488 6,1,5,2,6,1,6,6,7,3,5,0,2,8,3,2,1,2,5,6,9,3,0,0,9,6,9,9,5,3,6,9,4,2, %U A272488 9,5,2,7,4,0,4,1,5,5,1,9,9,1,2,8,3,8,0,3,6,4,6,7,7,0,5,1,0,9,5,0,8,0,9,4,7 %N A272488 Decimal expansion of the edge length of a regular 9-gon with unit circumradius. %C A272488 The edge length e(m) of a regular m-gon is e(m) = 2*sin(Pi/m). In this case, m = 9, and the constant, a = e(9), 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 A272488 Stanislav Sykora, <a href="/A272488/b272488.txt">Table of n, a(n) for n = 0..2000</a> %H A272488 Wikipedia, <a href="http://en.wikipedia.org/wiki/Constructible_number">Constructible number</a> %H A272488 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a> %H A272488 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a> %F A272488 Equals 2*sin(Pi/9) = 2*cos(Pi*7/18) = 2*A019829. %F A272488 Equals Im((4+4*sqrt(3)*i)^(1/3)). - _Gerry Martens_, Mar 19 2024 %F A272488 A root of x^6 -6*x^4 +9*x^2 -3 =0. - _R. J. Mathar_, Aug 29 2025 %e A272488 0.6840402866513374660881992293645191615261667350283212569300969953... %t A272488 RealDigits[N[2Sin[Pi/9], 100]][[1]] (* _Robert Price_, May 01 2016 *) %o A272488 (PARI) 2*sin(Pi/9) %Y A272488 Cf. A004169, A019434. %Y A272488 Edge lengths of nonconstructible n-gons: A272487 (n=7), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19). %K A272488 nonn,cons,easy,changed %O A272488 0,1 %A A272488 _Stanislav Sykora_, May 01 2016