

A010466


Decimal expansion of square root of 8.


51



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

1,1


COMMENTS

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 eighthsmallest triangle with integer side lengths (2, 3, 3), or the seventhsmallest 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 8gon with circumradius =1.  R. J. Mathar, Aug 24 2023


REFERENCES

S. R. Finch, Moving Sofa Constant, Sect. 8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519523, 2003.


LINKS



FORMULA

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*n3))*binomial(1/2,n). Cf. A002580 and A175576.
Equals 4*hypergeom([1/2, 3/4], [5/4], 1). (End)


EXAMPLE

2.828427124746190097603377448419396157139343750753896146353359475981464...
Sqrt(8) = sqrt(1+2*i*sqrt(2)) + sqrt(12*i*sqrt(2)) = sqrt(1/2+2*i*sqrt(3)) + sqrt(1/22*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


MAPLE



MATHEMATICA



PROG

(PARI) default(realprecision, 20080); x=sqrt(8); for (n=1, 20000, d=floor(x); x=(xd)*10; write("b010466.txt", n, " ", d)); \\ Harry J. Smith, Jun 02 2009
(Magma) SetDefaultRealField(RealField(100)); Sqrt(8); // Vincenzo Librandi, Feb 13 2020


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



