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 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 (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... MAPLE evalf[100](sqrt(12)); # Muniru A Asiru, Feb 12 2019 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 STATUS approved

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Last modified October 18 01:04 EDT 2019. Contains 328135 sequences. (Running on oeis4.)