This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A112628 #35 Feb 16 2025 08:32:59
%S A112628 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,
%T A112628 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,
%U A112628 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
%N A112628 Decimal expansion of 2*sqrt(2)/Pi.
%C A112628 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.).
%C A112628 The area of a regular octagon circumscribed in a unit-area circle. - _Amiram Eldar_, Nov 05 2020
%H A112628 G. C. Greubel, <a href="/A112628/b112628.txt">Table of n, a(n) for n = 0..10000</a>
%H A112628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BuffonsNeedleProblem.html">Buffon's needle problem</a>.
%H A112628 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedDiameter.html">Generalized Diameter</a>.
%H A112628 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A112628 Equals Product_{n>=1} (1-1/(4*n)^2). - _Bruno Berselli_, Apr 02 2013
%F A112628 Equals sinc(Pi/4). - _Peter Luschny_, Oct 04 2019
%F A112628 Equals Product_{k>=3} cos(Pi/2^k). - _Amiram Eldar_, Aug 24 2020
%e A112628 0.9003163161571060695551991910067405826645741499552206255714374712314587307...
%t A112628 RealDigits[2 Sqrt[2]/Pi, 10, 110][[1]] (* _Bruno Berselli_, Apr 02 2013 *)
%t A112628 (* From the second comment: *) RealDigits[N[Product[1 - 1/(4 n)^2, {n, 1, Infinity}], 110]][[1]] (* _Bruno Berselli_, Apr 02 2013 *)
%o A112628 (PARI) 2*sqrt(2)/Pi
%o A112628 (Magma) R:= RealField(100); 2*Sqrt(2)/Pi(R); // _G. C. Greubel_, Aug 17 2018
%Y A112628 Cf. A060294 (2/Pi), A089491 (3/Pi), A224268.
%K A112628 cons,nonn
%O A112628 0,1
%A A112628 _Rick L. Shepherd_, Jan 11 2006