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 A272487 #32 Aug 29 2025 14:05:50 %S A272487 8,6,7,7,6,7,4,7,8,2,3,5,1,1,6,2,4,0,9,5,1,5,3,6,6,6,5,6,9,6,7,1,7,5, %T A272487 0,9,2,1,9,9,8,1,4,5,5,5,7,4,9,1,9,7,5,2,8,8,9,0,9,4,6,0,7,0,6,4,4,0, %U A272487 6,5,0,3,3,0,6,3,9,6,8,4,3,0,4,1,5,6,8,0,4,3,5,4,8,9,1,2,2,0,4,1,7,7,4,8,8 %N A272487 Decimal expansion of the edge length of a regular heptagon with unit circumradius. %C A272487 The edge length e(m) of a regular m-gon is e(m) = 2*sin(Pi/m). In this case, m = 7, and the constant, a = e(7), is the smallest m for which e(m) 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 A272487 Stanislav Sykora, <a href="/A272487/b272487.txt">Table of n, a(n) for n = 0..2000</a> %H A272487 Wikipedia, <a href="http://en.wikipedia.org/wiki/Constructible_number">Constructible number</a> %H A272487 Wikipedia, <a href="http://en.wikipedia.org/wiki/Heptagon">Heptagon</a> %H A272487 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a> %H A272487 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a> %F A272487 Equals 2*sin(Pi/7) = 2*cos(Pi*5/14). %F A272487 Equals i^(-5/7) + i^(5/7). - _Gary W. Adamson_, Feb 12 2022 %F A272487 One of the 6 real-valued roots of x^6 -7*x^4 +14*x^2 -7 =0. - _R. J. Mathar_, Aug 29 2025 %e A272487 0.8677674782351162409515366656967175092199814555749197528890946... %t A272487 N[2*Sin[Pi/7], 25] (* _G. C. Greubel_, May 01 2016 *) %t A272487 RealDigits[2*Sin[Pi/7],10,120][[1]] (* _Harvey P. Dale_, Mar 07 2020 *) %o A272487 (PARI) 2*sin(Pi/7) %Y A272487 Cf. A004169, A019434. %Y A272487 Cf. A160389. %Y A272487 Edge lengths of nonconstructible n-gons: A272488 (n=9), A272489 (n=11), A272490 (n=13), A255241 (n=14), A130880 (n=18), A272491 (n=19). %K A272487 nonn,cons,easy,changed %O A272487 0,1 %A A272487 _Stanislav Sykora_, May 01 2016