A020769 Decimal expansion of 1/sqrt(12) = 1/(2*sqrt(3)).

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

Offset

0,1

Comments

Center density of densest packing of equal circles in two dimensions (achieved for example by the A2 lattice).

Let a equal the length of one side of an equilateral triangle and let b equal the radius of the circle inscribed in that triangle. This sequence gives the decimal expansion of b/a. - Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Feb 20 2004

The constant (3+sqrt 3)/6, which is 0.5 larger than this, plays a role in Borsuk's conjecture. - Arkadiusz Wesolowski, Mar 17 2014

This is also the distance between the pivot point and the center of a thin, straight rod of length 1 that minimizes the oscillation period of such a rod as a pendulum in a gravitational field. See "Dr. Viv's" YouTube video for a derivation. - Hugo Pfoertner, Apr 06 2026

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer, 3rd. ed., 1998. See p. xix.

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

J. H. Conway and N. J. A. Sloane, What are all the best sphere packings in low dimensions?, Discr. Comp. Geom., 13 (1995), 383-403.

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

N. J. A. Sloane and Andrey Zabolotskiy, Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural).

Learn Physics with Dr. Viv!, Minimum oscillation period of physical pendulum, YouTube video, 2020.

Wikipedia, Borsuk's conjecture

Index entries for algebraic numbers, degree 2

Example

0.28867513459481288225457439025097872782380087563506343800930116324198883615...

Mathematica

RealDigits[N[1/Sqrt[12], 200]] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)

Prog

(PARI) 1/sqrt(12) \\ Charles R Greathouse IV, Oct 31 2014

Crossrefs

Related constants: A020789, A093766, A093825, A222066, A222067, A222068, A222069, A222070, A222071, A222072, A260646.

Sequence in context: A198367 A395321 A021780 * A105388 A178247 A048651

Adjacent sequences: A020766 A020767 A020768 * A020770 A020771 A020772

Keyword

nonn,cons

Author

N. J. A. Sloane

Status

approved