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 A256853 #25 Aug 29 2025 13:59:45 %S A256853 6,1,8,1,8,2,4,1,9,3,7,7,2,9,0,0,1,2,7,2,1,3,7,4,4,0,5,9,6,1,9,7,6,3, %T A256853 6,1,4,9,4,1,7,1,3,3,4,8,1,3,4,3,5,8,0,9,8,3,8,6,8,6,4,2,5,5,6,6,9,7, %U A256853 7,1,0,7,1,2,3,3,5,8,4,6,6,4,7,6,6,3,5,9,5,5,3,3,8,9,0,7,9,1,8,4,0,9,9,0,2 %N A256853 Decimal expansion of the area of a unit 9-gon. %C A256853 From _Michal Paulovic_, May 09 2024: (Start) %C A256853 This constant multiplied by the square of the side length of a regular enneagon equals the area of that enneagon. %C A256853 9^2 divided by this constant equals 36 * tan(Pi/9) = 13.10292843... which is the perimeter and the area of an equable enneagon with its side length 4 * tan(Pi/9) = 1.45588093... . (End) %H A256853 Stanislav Sykora, <a href="/A256853/b256853.txt">Table of n, a(n) for n = 1..2000</a> %H A256853 Wikipedia, <a href="http://en.wikipedia.org/wiki/Nonagon">Nonagon</a> %H A256853 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_polygon">Regular polygon</a> %H A256853 <a href="/index/Al#algebraic_06">Index entries for algebraic numbers, degree 6</a> %F A256853 Equals (p/4)*cot(Pi/p), with p = 9. %F A256853 From _Michal Paulovic_, May 09 2024: (Start) %F A256853 Equals 9 * sqrt(2 / (1 - sin(5 * A000796 / 18)) - 1) / 4. %F A256853 Equals 9 * sqrt(2 / (1 - sin(5 * A019669 / 9)) - 1) / 4. %F A256853 Equals 9 * sqrt(2 / (1 - sin(5 * A019670 / 6)) - 1) / 4. %F A256853 Equals 9 * sqrt(2 / (1 - sin(5 * A019673 / 3)) - 1) / 4. %F A256853 Equals 9 * sqrt(2 / (1 - sin(5 * A019676 / 2)) - 1) / 4. %F A256853 Equals 9 * sqrt(2 / (1 - sin(50 * A019685)) - 1) / 4. %F A256853 Equals 9 * sqrt(2 / (1 - sin(5 * Pi / 18)) - 1) / 4. %F A256853 Equals 9 * sqrt(4 / (2 - i^(4/9) - i^(-4/9)) - 1) / 4. %F A256853 Equals 9 * sqrt(1 / (8 - (-32 + sqrt(-3072))^(1/3) - (-32 - sqrt(-3072))^(1/3)) - 1/16). (End) %F A256853 Largest of the 6 real-valued roots of 4096*x^6 -186624*x^4 +1154736*x^2 -177147 =0. - _R. J. Mathar_, Aug 29 2025 %e A256853 6.181824193772900127213744059619763614941713348134358098386864... %p A256853 evalf(9 / (4 * tan(Pi/9)), 100); # _Michal Paulovic_, May 09 2024 %t A256853 RealDigits[(9/4)*Cot[Pi/9], 10, 50][[1]] (* _G. C. Greubel_, Jul 03 2017 *) %o A256853 (PARI) p=9; a=(p/4)*cotan(Pi/p) \\ Use realprecision in excess %Y A256853 Cf. A000796, A019669, A019670, A019673, A019676, A019685, A019968, A120011 (p=3), A102771 (p=5), A104956 (p=6), A178817 (p=7), A090488 (p=8), A178816 (p=10), A256854 (p=11), A178809 (p=12). %K A256853 nonn,cons,changed %O A256853 1,1 %A A256853 _Stanislav Sykora_, Apr 12 2015