A112628 Decimal expansion of 2*sqrt(2)/Pi.

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

Offset: 0

Author

Rick L. Shepherd, Jan 11 2006

Keywords

• cons
• nonn

Comments

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

Examples

			0.9003163161571060695551991910067405826645741499552206255714374712314587307...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Buffon's needle problem.
• Eric Weisstein's World of Mathematics, Generalized Diameter.
• Index entries for transcendental numbers

Crossrefs

Cf. A060294 (2/Pi), A089491 (3/Pi), A224268.

Programs

Magma

R:= RealField(100); 2*Sqrt(2)/Pi(R); // G. C. Greubel, Aug 17 2018

Mathematica

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 *)

PARI

2*sqrt(2)/Pi

Formula

Equals Product_{n>=1} (1-1/(4*n)^2). - Bruno Berselli, Apr 02 2013

Equals sinc(Pi/4). - Peter Luschny, Oct 04 2019

Equals Product_{k>=3} cos(Pi/2^k). - Amiram Eldar, Aug 24 2020