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A154739
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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.
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8
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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, 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, 8, 9, 7, 3, 5, 4, 1, 0, 1, 2, 6, 6, 6, 4, 7, 7, 8, 2, 6, 1, 4, 9, 5
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OFFSET
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0,1
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COMMENTS
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A root of 2*x^4 - 4*x^2 + 1 = 0.
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REFERENCES
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C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5
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LINKS
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EXAMPLE
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0.541196100146196984399723205366...
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MATHEMATICA
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nmax = 1000; First[ RealDigits[ Sqrt[ 1 - 1/Sqrt[2] ], 10, nmax] ]
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PROG
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CROSSREFS
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Cf. A154740, A154741 and A154742 for the continued fraction and the numerators and denominators of the convergents.
Cf. A085565 for 1.311028777..., the first-quadrant arc length of the unit lemniscate.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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