

A010469


Decimal expansion of square root of 12.


15



3, 4, 6, 4, 1, 0, 1, 6, 1, 5, 1, 3, 7, 7, 5, 4, 5, 8, 7, 0, 5, 4, 8, 9, 2, 6, 8, 3, 0, 1, 1, 7, 4, 4, 7, 3, 3, 8, 8, 5, 6, 1, 0, 5, 0, 7, 6, 2, 0, 7, 6, 1, 2, 5, 6, 1, 1, 1, 6, 1, 3, 9, 5, 8, 9, 0, 3, 8, 6, 6, 0, 3, 3, 8, 1, 7, 6, 0, 0, 0, 7, 4, 1, 6, 2, 2, 9, 2, 3, 7, 3, 5, 1, 4, 4, 9, 7, 1, 5
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OFFSET

1,1


COMMENTS

3+sqrt(12) is the ratio of the radii of the three identical kissing circles to that of their inner Soddy circle.  Lekraj Beedassy, Mar 04 2006
sqrt(12)3 = 2*sqrt(3)3 is the area of the largest equilateral triangle that can be inscribed in a unit square (as stated in MathWorld/Weisstein link).  Rick L. Shepherd, Jun 24 2006
Continued fraction expansion is 3 followed by {2, 6} repeated.  Harry J. Smith, Jun 02 2009
Where 1, 5, 7, 11 are the automorphisms of cyclic group Z/12Z, and where 360 degrees/12 = 30 degrees, then, with reference to the unit circle, sqrt(12) can be constructed thusly: cos (1 * 30 degrees) + cos (5 * 30 degrees) + cos(7 * 30 degrees) + cos(11 * 30 degrees) = sqrt(3)/2 + sqrt(3)/2 + sqrt(3)/2 + sqrt(3)/2 = 2*sqrt(3) = sqrt(12).  Raphie Frank, Dec 26 2012
Surface of a regular octahedron with unit edge, and twice the surface of a regular tetrahedron with unit edge.  Stanislav Sykora, Nov 21 2013
Imaginary part of the square of a complex cubic root of 64 (real part is 2).  Alonso del Arte, Jan 13 2014


LINKS

Harry J. Smith, Table of n, a(n) for n = 1..20000
Eric Weisstein's World of Mathematics, Equilateral Triangle.
Wikipedia, Octahedron
Wikipedia, Platonic solid


FORMULA

Equals 2*sqrt(3) = 2*A002194.  Rick L. Shepherd, Jun 24 2006


EXAMPLE

3.4641016151377545870548926830...


MATHEMATICA

RealDigits[N[Sqrt[12], 200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)


PROG

(PARI) { default(realprecision, 20080); x=sqrt(12); for (n=1, 20000, d=floor(x); x=(xd)*10; write("b010469.txt", n, " ", d)); } \\ Harry J. Smith, Jun 02 2009


CROSSREFS

Cf. A040008.
Cf. A002194, A120683.
Cf. A040008 Continued fraction.  Harry J. Smith, Jun 02 2009
Cf. A002194 (surface of tetrahedron), A010527 (surface of icosahedron/10), A131595 (surface of dodecahedron).  Stanislav Sykora, Nov 30 2013
Sequence in context: A185261 A263354 A212482 * A136248 A175653 A101432
Adjacent sequences: A010466 A010467 A010468 * A010470 A010471 A010472


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane


STATUS

approved



