A396022 - OEIS

%I #8 May 17 2026 15:32:40

%S 5,4,3,3,8,8,9,6,5,2,2,3,0,6,7,1,8,8,9,2,6,5,6,7,3,2,4,4,9,6,7,1,3,8,

%T 6,9,7,3,5,0,6,2,8,2,8,9,6,9,7,1,8,0,5,3,8,8,8,1,9,4,0,5,5,9,2,5,6,5,

%U 8,2,7,7,9,4,8,2,1,4,6,5,6,4,2,9,7,4,8,2,9,9,9,7,1,0,2,6,7,5,7,1,6,1,5,3,3

%N Decimal expansion of (2+sqrt(2))/(2*Pi).

%C The probability that Buffon's needle (see A060294), bent at its midpoint at a 90 degrees angle, 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 Robert Nelson, <a href="https://www.jstor.org/stable/3026739">Pictures, Probability, and Paradox</a>, The Two-Year College Mathematics Journal, Vol. 10, No. 3 (1979), pp. 182-190. See Problem 6, pp. 187-188.

%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&#39;s_needle_problem">Buffon's needle problem</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 0.543388965223067188926567324496713869735062828969718...

%t RealDigits[(2+Sqrt[2])/(2*Pi), 10, 120][[1]]

%o (PARI) (2+sqrt(2))/(2*Pi)

%Y Cf. A060294, A089491, A396023.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, May 14 2026