%I A003957
%S A003957 7,3,9,0,8,5,1,3,3,2,1,5,1,6,0,6,4,1,6,5,5,3,1,2,0,8,7,6,7,3,8,7,3,4,0,
               4,
%T A003957 0,1,3,4,1,1,7,5,8,9,0,0,7,5,7,4,6,4,9,6,5,6,8,0,6,3,5,7,7,3,2,8,4,6,5,
               4,
%U A003957 8,8,3,5,4,7,5,9,4,5,9,9,3,7,6,1,0,6,9,3,1,7,6,6,5,3,1,8,4,9,8,0,1,2,4,
               6
%N A003957 Decimal expansion of root of cos x = x.
%C A003957 The unique root of cos(x)=x has been called the Dottie number. This root 
               is a simple nontrivial example of a universal attracting fixed point. 
               The story of how the Dottie number got its name and mathematical 
               concepts relating to this value can be used as teaching tools. Pedagogical 
               examples are given for several courses ranging from Calculus I to 
               Complex Analysis. [Kaplan] - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Apr 04 2007
%D A003957 Samuel R. Kaplan, The Dottie Number, Math. Magazine, 80 (No. 1, 2007), 
               73-74.
%H A003957 Ben Branman (137ben(AT)comcast.net), Apr 12 2008, <a href="b003957.txt">
               Table of n, a(n) for n = 0..499</a>
%H A003957 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Cosine.html">Cosine</a>
%H A003957 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlmostInteger.html">Almost Integer</a>
%H A003957 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DottieNumber.html">Dottie Number</a>
%e A003957 0.7390851332151606...
%t A003957 RealDigits[ FindRoot[ Cos[x] == x, {x, {.7, 1} }, WorkingPrecision -> 
               120] [[1, 2] ]] [[1]]
%t A003957 FindRoot[Cos[x] == x, {x, {.7, 1}}, WorkingPrecision -> 500][[1, 2]]][[1]] 
               - Ben Branman (137ben(AT)comcast.net), Apr 12 2008
%Y A003957 Sequence in context: A011330 A093587 A072334 this_sequence A021579 A139788 
               A093525
%Y A003957 Adjacent sequences: A003954 A003955 A003956 this_sequence A003958 A003959 
               A003960
%K A003957 cons,nonn
%O A003957 0,1
%A A003957 Leonid Broukhis (leo(AT)mailcom.com)
%E A003957 More terms from David W. Wilson (davidwwilson(AT)comcast.net)