%I #53 Aug 21 2023 11:26:21

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

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

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

%N Decimal expansion of square root of 27.

%C Continued fraction expansion is 5 followed by {5, 10} repeated (A040021). - _Harry J. Smith_, Jun 04 2009

%C 6 + sqrt(27) represents the surface of a dodecahedron of side equal to one. S = 3*a^2(2 + sqrt(3)) with a = 1. - _Vincenzo Librandi_, Jul 10 2010

%C sqrt(27) is the perimeter of an equilateral triangle whose incircle's diameter is 1. - _Martin Janecke_, May 31 2016

%C If r = 2*a * sin(3t)/sin(2t) and x*(x^2+y^2) = a * (3x^2-y^2) are respectively a polar equation and a Cartesian equation of the Maclaurin trisectrix, then sqrt(27) * a^2 = area of the loop of this trisectrix = area between the curve and its asymptote (see Mathcurve link). - _Bernard Schott_, Jul 14 2020

%C Area of a regular hexagon with side length sqrt(2). - _Christoph B. Kassir_, Sep 29 2022

%C The solution of x^sqrt(3)=sqrt(3)^x, see e.g. A360148. - _R. J. Mathar_, Mar 24 2023

%H Harry J. Smith, <a href="/A010482/b010482.txt">Table of n, a(n) for n = 1..20000</a>

%H Robert Ferréol, <a href="https://mathcurve.com/courbes2d.gb/maclaurin/maclaurin.shtml">MacLaurin trisectrix</a>, Mathcurve.

%H <a href="https://oeis.org/wiki/Index_to_OEIS:_Section_Cu">Index to sequences related to curves</a>.

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%F Equals 3*sqrt(3) = 3 * A002194. - _Bernard Schott_, Jul 14 2020

%F Equals 2 * A104956. - _Christoph B. Kassir_, Oct 02 2022

%e 5.196152422706631880582339024517617100828415761431141884167420938355799....

%t RealDigits[N[Sqrt[27], 200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 22 2011 *)

%o (PARI) default(realprecision, 20080); x=sqrt(27); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010482.txt", n, " ", d)); \\ _Harry J. Smith_, Jun 04 2009

%Y Cf. A040021 (continued fraction), A248254 (Egyptian fraction).

%Y Cf. A104956 (half), A002194 (sqrt(3)).

%K nonn,cons,easy

%O 1,1

%A _N. J. A. Sloane_