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%I #13 Sep 23 2017 03:17:19
%S 5,4,1,1,9,6,1,0,0,1,4,6,1,9,6,9,8,4,3,9,9,7,2,3,2,0,5,3,6,6,3,8,9,4,
%T 2,0,0,6,1,0,7,2,0,6,3,3,7,8,0,1,5,4,4,4,6,8,1,2,9,7,0,9,5,6,5,2,9,8,
%U 8,9,7,3,5,4,1,0,1,2,6,6,6,4,7,7,8,2,6,1,4,9,5
%N Decimal expansion of sqrt(1 - 1/sqrt(2)), the abscissa of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
%C A root of 2*x^4 - 4*x^2 + 1 = 0.
%D C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5
%H G. C. Greubel, <a href="/A154739/b154739.txt">Table of n, a(n) for n = 0..5000</a>
%e 0.541196100146196984399723205366...
%t nmax = 1000; First[ RealDigits[ Sqrt[ 1 - 1/Sqrt[2] ], 10, nmax] ]
%o (PARI) sqrt(1 - 1/sqrt(2)) \\ _G. C. Greubel_, Sep 23 2017
%Y Cf. A154743 for the ordinate and A154747 for the radius vector.
%Y Cf. A154740, A154741 and A154742 for the continued fraction and the numerators and denominators of the convergents.
%Y Cf. A085565 for 1.311028777..., the first-quadrant arc length of the unit lemniscate.
%K nonn,cons,easy
%O 0,1
%A _Stuart Clary_, Jan 14 2009
%E Offset corrected by _R. J. Mathar_, Feb 05 2009
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