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A010469 Decimal expansion of square root of 12. 14
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 (list; constant; graph; refs; listen; history; text; internal format)
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=(x-d)*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

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Last modified March 30 01:16 EDT 2017. Contains 284295 sequences.