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A002194
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Decimal expansion of square root of 3.
(Formerly M4326 N1812)
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51
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1, 7, 3, 2, 0, 5, 0, 8, 0, 7, 5, 6, 8, 8, 7, 7, 2, 9, 3, 5, 2, 7, 4, 4, 6, 3, 4, 1, 5, 0, 5, 8, 7, 2, 3, 6, 6, 9, 4, 2, 8, 0, 5, 2, 5, 3, 8, 1, 0, 3, 8, 0, 6, 2, 8, 0, 5, 5, 8, 0, 6, 9, 7, 9, 4, 5, 1, 9, 3, 3, 0, 1, 6, 9, 0, 8, 8, 0, 0, 0, 3, 7, 0, 8, 1, 1, 4, 6, 1, 8, 6, 7, 5, 7, 2, 4, 8, 5, 7, 5, 6, 7, 5, 6, 2, 6, 1, 4, 1, 4, 1, 5, 4
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| "The square root of 3, the 2nd number, after root 2, to be proved irrational, by Theodorus."
Length of a diagonal between any vertex of the unit cube and the one corresponding (opposite) vertex not part of the three faces meeting at the original vertex. (Diagonal is hypotenuse of a triangle with sides 1 and sqrt(2)). Hence the diameter of the sphere circumscribed around the unit cube; the ratio of the diameter of any sphere to the edge length of its inscribed cube. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 09 2005
The square root of 3 is the length of the minimal Y-shaped (symmetrical) network linking three points unit distance apart. - Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 12 2006
Continued fraction expansion is 1 followed by {1, 2} repeated. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
Also, tan(pi/3) = 2 sin(pi/3). - M. F. Hasler, Oct 27 2011
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REFERENCES
| M. F. Jones, 22900D approximations to the square roots of the primes less than 100, Math. Comp., 22 (1968), 234-235.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Uhler, Horace S.; Approximations exceeding 1300 decimals for sqrt 3, 1/sqrt 3, sin(pi/3) and distribution of digits in them. Proc. Nat. Acad. Sci. U. S. A. 37, (1951). 443-447.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 23.
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 1..20000
R. J. Nemiroff and J. Bonnell, The first 1 million digits of the square root of 3
S. Plouffe, Plouffe's Inverter, The square root of 3 to 10 million digits
Eric Weisstein's World of Mathematics, Square Root
Eric Weisstein's World of Mathematics, Theodorus's Constant
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EXAMPLE
| 1.73205080756887729352744634150587236694280525381038062805580697945193...
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MATHEMATICA
| RealDigits[ N[ Sqrt[3], 100]] [[1]]
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PROG
| (PARI) { default(realprecision, 20080); x=(sqrt(3)); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b002194.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
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CROSSREFS
| Cf. A040001 Continued fraction.
Sequence in context: A133722 A204155 A160390 * A033327 A024584 A132713
Adjacent sequences: A002191 A002192 A002193 * A002195 A002196 A002197
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KEYWORD
| cons,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 07 2000
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