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A010466
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Decimal expansion of square root of 8.
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51
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2, 8, 2, 8, 4, 2, 7, 1, 2, 4, 7, 4, 6, 1, 9, 0, 0, 9, 7, 6, 0, 3, 3, 7, 7, 4, 4, 8, 4, 1, 9, 3, 9, 6, 1, 5, 7, 1, 3, 9, 3, 4, 3, 7, 5, 0, 7, 5, 3, 8, 9, 6, 1, 4, 6, 3, 5, 3, 3, 5, 9, 4, 7, 5, 9, 8, 1, 4, 6, 4, 9, 5, 6, 9, 2, 4, 2, 1, 4, 0, 7, 7, 7, 0, 0, 7, 7, 5, 0, 6, 8, 6, 5, 5, 2, 8, 3, 1, 4, 5, 4, 7
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OFFSET
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1,1
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COMMENTS
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Sqrt(8) = 2*sqrt(2) is the length of the longest (rigid) ladder that can be carried horizontally around a right angled corner in a hallway of unit width. - Lekraj Beedassy, Apr 19 2006
Continued fraction expansion is 2 followed by {1, 4} repeated. - Harry J. Smith, Jun 05 2009
Also 2*sqrt(2) is the ratio of the perimeter of a square to its diameter (diagonal length). - Rick L. Shepherd, Dec 29 2016
Uchiyama shows that every interval (n, n + c*n^(1/4)) contains an integer that is the sum of two squares, where c = 2^(3/2). - Michel Marcus, Jan 03 2018
This is the area of the eighth-smallest triangle with integer side lengths (2, 3, 3), or the seventh-smallest triangle if two smaller triangles with the same area are counted only once (see A331251). - Hugo Pfoertner, Feb 12 2020
Diameter of a sphere whose surface area equals 8*Pi. More generally, the square root of x is also the diameter of a sphere whose surface area equals x*Pi. - Omar E. Pol, Feb 13 2020
Sqrt(8) = area between the curves y = sin(x) and y = cos(x) for Pi/4 < x < 5 Pi/4; this is one of infinitely many congruent convex regions bounded by the two curves. - Clark Kimberling, May 03 2020
Area of the regular 8-gon with circumradius =1. - R. J. Mathar, Aug 24 2023
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REFERENCES
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S. R. Finch, Moving Sofa Constant, Sect. 8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.
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LINKS
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FORMULA
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Equals 1 + Sum_{n>=1} ( Product_{k=1..n} (2k+1)/(4k) ). - Bruno Berselli, Mar 16 2014
Equals 3*Sum_{n >= 0} (1/(4*n+1) - 1/(4*n-3))*binomial(1/2,n). Cf. A002580 and A175576.
Equals 4*hypergeom([-1/2, -3/4], [5/4], -1). (End)
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EXAMPLE
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2.828427124746190097603377448419396157139343750753896146353359475981464...
Sqrt(8) = sqrt(1+2*i*sqrt(2)) + sqrt(1-2*i*sqrt(2)) = sqrt(1/2+2*i*sqrt(3)) + sqrt(1/2-2*i*sqrt(3)), where i=sqrt(-1). - Bruno Berselli, Nov 20 2012
1 + 3/4 + 3*5/(4*8) + 3*5*7/(4*8*12) + 3*5*7*9/(4*8*12*16) + ... - Bruno Berselli, Mar 16 2014
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MAPLE
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MATHEMATICA
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PROG
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(PARI) default(realprecision, 20080); x=sqrt(8); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010466.txt", n, " ", d)); \\ Harry J. Smith, Jun 02 2009
(Magma) SetDefaultRealField(RealField(100)); Sqrt(8); // Vincenzo Librandi, Feb 13 2020
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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