OFFSET
1,1
COMMENTS
Continued fraction expansion is 5 followed by {5, 10} repeated (A040021). - Harry J. Smith, Jun 04 2009
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
sqrt(27) is the perimeter of an equilateral triangle whose incircle's diameter is 1. - Martin Janecke, May 31 2016
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
Area of a regular hexagon with side length sqrt(2). - Christoph B. Kassir, Sep 29 2022
The solution of x^sqrt(3)=sqrt(3)^x, see e.g. A360148. - R. J. Mathar, Mar 24 2023
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..20000
Robert Ferréol, MacLaurin trisectrix, Mathcurve.
FORMULA
Equals 3*sqrt(3) = 3 * A002194. - Bernard Schott, Jul 14 2020
Equals 2 * A104956. - Christoph B. Kassir, Oct 02 2022
EXAMPLE
5.196152422706631880582339024517617100828415761431141884167420938355799....
MATHEMATICA
RealDigits[N[Sqrt[27], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2011 *)
PROG
(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
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved