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A010527
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Decimal expansion of sqrt(3)/2.
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38
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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
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0,1
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COMMENTS
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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
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REFERENCES
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A. O. Ivanov and A. A. Tuzhilin, "The Steiner ratio Gilbert-Pollak conjecture is still open", Algorithmica 62:1-2 (2012), pp. 630-632.
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LINKS
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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.
_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
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EXAMPLE
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0.86602540378443864676372317...
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MATHEMATICA
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RealDigits[N[Sqrt[3]/2, 200]][[1]] (*From Vladimir Joseph Stephan Orlovsky, Feb 21 2011*)
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PROG
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(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)); } \\ From Harry J. Smith, Jun 02 2009
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CROSSREFS
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Cf. A010153.
Sequence in context: A197329 A046266 A165104 * A102887 A067970 A003675
Adjacent sequences: A010524 A010525 A010526 * A010528 A010529 A010530
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KEYWORD
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nonn,cons,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Corrected last term and added more terms. Harry J. Smith, Jun 02 2009
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STATUS
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approved
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