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%I #76 Nov 27 2023 07:56:46
%S 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,
%T 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,
%U 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
%N Decimal expansion of square root of 12.
%C 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
%C 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
%C Continued fraction expansion is 3 followed by {2, 6} repeated (A040008). - _Harry J. Smith_, Jun 02 2009
%C Surface of a regular octahedron with unit edge, and twice the surface of a regular tetrahedron with unit edge. - _Stanislav Sykora_, Nov 21 2013
%C Imaginary part of the square of a complex cubic root of 64 (real part is -2). - _Alonso del Arte_, Jan 13 2014
%H Harry J. Smith, <a href="/A010469/b010469.txt">Table of n, a(n) for n = 1..20000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EquilateralTriangle.html">Equilateral Triangle</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Octahedron">Octahedron</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F Equals 2*sqrt(3) = 2*A002194. - _Rick L. Shepherd_, Jun 24 2006
%e 3.4641016151377545870548926830...
%p evalf[100](sqrt(12)); # _Muniru A Asiru_, Feb 12 2019
%t RealDigits[N[Sqrt[12], 200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 21 2011 *)
%o (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
%Y Cf. A120683.
%Y Cf. A040008 (continued fraction), A041016 (numerators of convergents), A041017 (denominators).
%Y Cf. A002194 (surface of tetrahedron), A010527 (surface of icosahedron/10), A131595 (surface of dodecahedron).
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_
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