A010469 Decimal expansion of square root of 12.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

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 (A040008). - Harry J. Smith, Jun 02 2009

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

Examples

			3.4641016151377545870548926830...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 2.31.4 and 2.31.5, pp. 201-202.
• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 450.

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.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A120683.

Cf. A040008 (continued fraction), A041016 (numerators of convergents), A041017 (denominators).

Cf. A002194 (surface of tetrahedron), A010527 (surface of icosahedron/10), A131595 (surface of dodecahedron).

Programs

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 *)

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

Formula

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