

A010527


Decimal expansion of sqrt(3)/2.


60



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



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
Also the ratio between the height and the pitch, used in the Unified Thread Standard (UTS).  Enrique Pérez Herrero, Nov 13 2014
Area of a 306090 triangle with shortest side equal to 1.  Wesley Ivan Hurt, Apr 09 2016


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
Wikipedia, Unified Thread Standard


FORMULA

Equals A002194/2.  Stanislav Sykora, Nov 30 2013
From Amiram Eldar, Jun 29 2020: (Start)
Equals sin(Pi/3) = cos(Pi/6).
Equals Integral_{x=0..Pi/3} cos(x) dx. (End)


EXAMPLE

0.86602540378443864676372317...


MAPLE

Digits:=100: evalf(sqrt(3)/2); # Wesley Ivan Hurt, Apr 09 2016


MATHEMATICA

RealDigits[N[Sqrt[3]/2, 200]][[1]] (* 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)); } \\ Harry J. Smith, Jun 02 2009
(PARI) sqrt(3)/2 \\ Michel Marcus, Apr 10 2016
(MAGMA) SetDefaultRealField(RealField(100)); Sqrt(3)/2; // G. C. Greubel, Nov 02 2018


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
Cf. A126664, A144535/A144536 (convergents).
Sequence in context: A197329 A046266 A165104 * A270137 A269846 A316136
Adjacent sequences: A010524 A010525 A010526 * A010528 A010529 A010530


KEYWORD

nonn,cons,easy,changed


AUTHOR

N. J. A. Sloane


EXTENSIONS

Last term corrected and more terms added by Harry J. Smith, Jun 02 2009


STATUS

approved



