A396028 - OEIS

%I #7 May 16 2026 04:52:39

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

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

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

%N Decimal expansion of the probability that Buffon's needle will not land on any line when dropped on a triangular tiling in which the altitude of each triangle equals the length of the needle.

%H A. A. Markoff (Andrey Andreyevich Markov), <a href="https://archive.org/details/wahrscheinlich00markrich/page/n182/mode/1up">Wahrscheinlichkeitsrechnung</a>, Leipzig und Berlin: B. G. Teubner, 1912, pp. 169-173.

%H Michael D. Perlman and Michael J. Wichura, <a href="https://www.jstor.org/stable/2683484">Sharpening Buffon's Needle</a>, The American Statistician, Vol. 29, No. 4 (1975), pp. 157-163.

%H Enis Siniksaran, <a href="https://doi.org/10.3888/tmj.11.1-4">Throwing Buffon's Needle with Mathematica</a>, The Mathematica Journal, Vol. 11, No. 1 (2008), pp. 71-90.

%H J. V. Uspensky, <a href="https://archive.org/details/dli.ernet.233593/page/258/mode/1up">Introduction To Mathematical Probability</a>, Mcgraw Hill Book Co. Inc., 1937, p. 258, Problem 8.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Buffon-LaplaceNeedleProblem.html">Buffon-Laplace Needle Problem</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Buffon&#39;s_needle_problem">Buffon's needle problem</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Triangular_tiling">Triangular tiling</a>.

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

%F Equals 3/2 - 3*(8-sqrt(3))/(4*Pi).

%F Equals 1/4 - A396029.

%F Equals 1 - A396029 - A102519 - (A240935 - 1/4).

%e 0.0036373544636000079068897132645547366345241113895031...

%t RealDigits[3/2 - 3*(8-Sqrt[3])/(4*Pi), 10, 120, -1][[1]]

%o (PARI) 3/2 - 3*(8-sqrt(3))/(4*Pi)

%Y Cf. A060294, A089491, this constant (0 lines), A396029 (1 line), A102519 (2 lines), A240935 - 1/4 (3 lines).

%K nonn,cons

%O 0,3

%A _Amiram Eldar_, May 14 2026