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A010527 Decimal expansion of sqrt(3)/2. 55
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 30-60-90 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. 1-29.

A. O. Ivanov and A. A. Tuzhilin, The Steiner ratio Gilbert-Pollak conjecture is still open, Algorithmica 62:1-2 (2012), pp. 630-632.

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

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=(x-d)*10; write("b010527.txt", n, " ", d)); } \\ Harry J. Smith, Jun 02 2009

(PARI) sqrt(3)/2 \\ Michel Marcus, Apr 10 2016

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 * A270137 A269846 A102887

Adjacent sequences:  A010524 A010525 A010526 * A010528 A010529 A010530

KEYWORD

nonn,cons,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified December 6 15:10 EST 2016. Contains 278781 sequences.