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%I #7 May 16 2026 04:01:24
%S 5,2,0,9,5,2,2,5,3,4,6,8,4,6,6,2,1,4,4,2,5,5,2,6,4,5,3,1,6,4,4,8,4,0,
%T 0,1,8,7,7,6,3,6,8,4,0,8,2,5,4,0,5,9,9,5,1,8,6,5,5,2,7,5,1,9,0,6,1,3,
%U 9,8,3,7,1,9,2,9,2,3,9,5,2,5,6,2,6,4,6,1,5,3,3,8,3,7,4,9,8,4,7,1,3,9,3,9,0,1
%N Decimal expansion of (Pi+2)/Pi^2.
%C The probability that Buffon's needle (see A060294), bent at its midpoint at a uniformly random angle between 0 and 360 degrees, will land on a line when dropped onto a floor with parallel lines spaced at a distance equal to the length of the needle.
%H Uwe Bäsel, <a href="https://doi.org/10.5169/seals-630622">Buffon's problem with a pivot needle</a>, Elemente der Mathematik, Vol. 70, No. 2 (2015), pp. 67-70. See Remark 1, p. 70.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BuffonsNeedleProblem.html">Buffon's needle problem</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Buffon's_needle_problem">Buffon's needle problem</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F Equals A049541 + A185197.
%F Equals 1/A197724.
%e 0.520952253468466214425526453164484001877636840825405...
%t RealDigits[(Pi+2)/Pi^2, 10, 120][[1]]
%o (PARI) (Pi+2)/Pi^2
%Y Cf. A049541, A060294, A089491, A185197, A197724, A396022.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, May 14 2026