

A010527


Decimal expansion of sqrt(3)/2.


49



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

0,1


COMMENTS

This is the ratio of the height of an equilateral triangle to its base.
Essentially the same sequence arises from decimal expansion of square root of 75, which is 8.6602540378443864676372317...
The same as cos(30 degrees).  Kausthub Gudipati, Aug 15 2011
Also the real part of i^(1/3), the cubic root of i. [Stanislav Sykora, Apr 25 2012]
Gilbert & Pollak conjectured that this is the Steiner ratio rho_2, the least upper bound of the ratio of the length of the Steiner minimal tree to the length of the minimal tree in dimension 2. (See Ivanov & Tuzhilin for the status of this conjecture as of 2012.)  Charles R Greathouse IV, Dec 11 2012
Surface area of a regular icosahedron with unit edge is 5*sqrt(3), i.e., 10 times this constant.  Stanislav Sykora, Nov 29 2013
Circumscribed sphere radius for a cube with unit edges.  Stanislav Sykora, Feb 10 2014


LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000
E. N. Gilbert and H. O. Pollak, Steiner minimal trees, SIAM J. Appl. Math. 16, (1968), pp. 129.
A. O. Ivanov and A. A. Tuzhilin, The Steiner ratio GilbertPollak conjecture is still open, Algorithmica 62:12 (2012), pp. 630632.
Simon Plouffe, Plouffe's Inverter, sqrt(3)/2 to 10000 digits
Simon Plouffe, Sqrt(3)/2 to 5000 digits
Eric Weisstein's World of Mathematics, Lebesgue Minimal Problem
Wikipedia, Icosahedron
Wikipedia, Platonic solid


FORMULA

A002194/2.  Stanislav Sykora, Nov 30 2013


EXAMPLE

0.86602540378443864676372317...


MATHEMATICA

RealDigits[N[Sqrt[3]/2, 200]][[1]] (*From Vladimir Joseph Stephan Orlovsky, Feb 21 2011*)


PROG

(PARI) { default(realprecision, 20080); x=10*(sqrt(3)/2); for (n=0, 20000, d=floor(x); x=(xd)*10; write("b010527.txt", n, " ", d)); } \\ From Harry J. Smith, Jun 02 2009


CROSSREFS

Cf. A010153, Platonic solids surfaces: A002194 (tetrahedron), A010469 (octahedron), A131595 (dodecahedron). Stanislav Sykora, Nov 30 2013
Cf. Platonic solids circumradii: A010503 (octahedron), A019881 (icosahedron), A179296 (dodecahedron), A187110 (tetrahedron).  Stanislav Sykora, Feb 10 2014
Sequence in context: A197329 A046266 A165104 * A102887 A067970 A003675
Adjacent sequences: A010524 A010525 A010526 * A010528 A010529 A010530


KEYWORD

nonn,cons,easy,changed


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Corrected last term and added more terms. Harry J. Smith, Jun 02 2009


STATUS

approved



