A020769 - OEIS

%I #34 Dec 30 2023 09:52:10

%S 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,

%T 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,

%U 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

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

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

%C 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

%C 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

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

%H Ivan Panchenko, <a href="/A020769/b020769.txt">Table of n, a(n) for n = 0..1000</a>

%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1007/BF02574051">What are all the best sphere packings in low dimensions?</a>, Discr. Comp. Geom., 13 (1995), 383-403.

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>

%H N. J. A. Sloane and Andrey Zabolotskiy, <a href="/A093825/a093825_1.txt">Table of maximal density of a packing of equal spheres in n-dimensional Euclidean space (some values are only conjectural)</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Borsuk%27s_conjecture">Borsuk's conjecture</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%e 0.28867513459481288225457439025097872782380087563506343800930116324198883615...

%t RealDigits[N[1/Sqrt[12],200]] (* _Vladimir Joseph Stephan Orlovsky_, May 30 2010 *)

%o (PARI) 1/sqrt(12) \\ _Charles R Greathouse IV_, Oct 31 2014

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

%K nonn,cons

%O 0,1

%A _N. J. A. Sloane_