%I A002194 M4326 N1812
%S A002194 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,
%T A002194 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,
%U A002194 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
%N A002194 Decimal expansion of square root of 3.
%C A002194 "The square root of 3, the 2nd number, after root 2, to be proved irrational, 
               by Theodorus."
%C A002194 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
%C A002194 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
%C A002194 Continued fraction expansion is 1 followed by {1, 2} repeated. [From 
               Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 01 2009]
%D A002194 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002194 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002194 M. F. Jones, 22900D approximations to the square roots of the primes 
               less than 100, Math. Comp., 22 (1968), 234-235.
%D A002194 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.
%D A002194 David Wells, "The Penguin Dictionary of Curious and Interesting Numbers,
               " Revised Edition, Penguin Books, London, England, 1997, page 23.
%H A002194 Harry J. Smith, <a href="b002194.txt">Table of n, a(n) for n=1,...,20000</
               a>
%H A002194 R. J. Nemiroff and J. Bonnell, <a href="http://antwrp.gsfc.nasa.gov/htmltest/
               gifcity/sqrt3.1mil">The first 1 million digits of the square root 
               of 3</a>
%H A002194 S. Plouffe, Plouffe's Inverter, <a href="http://pi.lacim.uqam.ca/piDATA/
               sqrt3.txt">The square root of 3 to 10 million digits</a>
%H A002194 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SquareRoot.html">Link to a section of The World of Mathematics.</
               a>
%H A002194 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TheodorussConstant.html">Theodorus's Constant</a>
%e A002194 1.73205080756887729352744634150587236694280525381038062805580697945193301690880\
%e A002194 0037081146186757248575675626141415406703029969945094998952478811655512094373648\
%e A002194 5280932319023055820679748201010846749232650153123432669033228866506722546689218\
%e A002194 3797122704713166036786158801904998653737985938946765034750657605...
%t A002194 RealDigits[ N[ Sqrt[3], 100]] [[1]]
%o A002194 (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]
%Y A002194 Cf. A040001 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Jun 01 2009]
%Y A002194 Sequence in context: A021899 A133722 A160390 this_sequence A033327 A024584 
               A132713
%Y A002194 Adjacent sequences: A002191 A002192 A002193 this_sequence A002195 A002196 
               A002197
%K A002194 cons,nonn
%O A002194 1,2
%A A002194 N. J. A. Sloane (njas(AT)research.att.com).
%E A002194 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 07 2000