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 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 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 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/2, 200]][] (* 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 (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 EXTENSIONS Last term corrected and more terms added by Harry J. Smith, Jun 02 2009 STATUS approved

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Last modified July 10 05:51 EDT 2020. Contains 335572 sequences. (Running on oeis4.)