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A112628
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Decimal expansion of 2*sqrt(2)/Pi.
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6
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9, 0, 0, 3, 1, 6, 3, 1, 6, 1, 5, 7, 1, 0, 6, 0, 6, 9, 5, 5, 5, 1, 9, 9, 1, 9, 1, 0, 0, 6, 7, 4, 0, 5, 8, 2, 6, 6, 4, 5, 7, 4, 1, 4, 9, 9, 5, 5, 2, 2, 0, 6, 2, 5, 5, 7, 1, 4, 3, 7, 4, 7, 1, 2, 3, 1, 4, 5, 8, 7, 3, 0, 7, 1, 9, 0, 4, 6, 3, 4, 4, 9, 9, 8, 0, 8, 2, 7, 7, 7, 7, 5, 4, 0, 8, 2, 3, 4, 0, 9, 9, 7, 5, 5, 1
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OFFSET
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0,1
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COMMENTS
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Example of extension to Buffon's Needle Problem: The probability that the boundary of a square will intersect one of the parallel lines if the square's diagonal length l (almost) equals the distance d between each pair of lines. This follows directly from the Weisstein/MathWorld Buffon's Needle Problem link's statement P=p/(Pi*d), where P is the probability of intersection with any convex polygon's boundary if the generalized diameter of that polygon is less than d and p is the perimeter of the polygon. (Take d=l, then p=2*sqrt(2)*d.).
The area of a regular octagon circumscribed in a unit-area circle. - Amiram Eldar, Nov 05 2020
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LINKS
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FORMULA
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Equals Product_{k>=3} cos(Pi/2^k). - Amiram Eldar, Aug 24 2020
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EXAMPLE
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0.9003163161571060695551991910067405826645741499552206255714374712314587307...
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MATHEMATICA
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RealDigits[2 Sqrt[2]/Pi, 10, 110][[1]] (* Bruno Berselli, Apr 02 2013 *)
(* From the second comment: *) RealDigits[N[Product[1 - 1/(4 n)^2, {n, 1, Infinity}], 110]][[1]] (* Bruno Berselli, Apr 02 2013 *)
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PROG
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(PARI) 2*sqrt(2)/Pi
(Magma) R:= RealField(100); 2*Sqrt(2)/Pi(R); // G. C. Greubel, Aug 17 2018
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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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