

A089491


Decimal expansion of Buffon's constant 3/Pi.


23



9, 5, 4, 9, 2, 9, 6, 5, 8, 5, 5, 1, 3, 7, 2, 0, 1, 4, 6, 1, 3, 3, 0, 2, 5, 8, 0, 2, 3, 5, 0, 8, 6, 1, 7, 2, 2, 0, 6, 7, 5, 7, 8, 7, 4, 4, 4, 2, 7, 3, 8, 6, 9, 2, 4, 8, 6, 0, 0, 4, 0, 6, 4, 3, 5, 3, 3, 8, 0, 7, 8, 5, 8, 0, 5, 3, 5, 9, 2, 1, 0, 5, 4, 0, 6, 8, 2, 8, 1, 6, 5, 9, 7, 5, 1, 8, 5, 1, 5, 7, 3, 6, 4, 3, 7
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OFFSET

0,1


COMMENTS

Whereas 2/Pi (A060294) is the probability that a needle will land on one of many parallel lines, this is the probability that a needle will land on one of many lines making up a grid.
The probability that the boundary of an equilateral triangle will intersect one of the parallel lines if the triangle edge 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=3d.)  Rick L. Shepherd, Jan 11 2006
Related grid problems are discussed in the Weisstein/MathWorld BuffonLaplace Needle Problem link.  Rick L. Shepherd, Jan 11 2006


REFERENCES

Joe Portney, Portney's Ponderables, Litton Systems, Inc., Appendix 2, 'Buffon's Needle' by Lawrence R. Weill, 200, pp. 135138.


LINKS

Table of n, a(n) for n=0..104.
Harry Khamis, Buffon's Needle Problem [Broken link]
Kevin Peterson, A Problem in Geometric Probability: Buffon's Needle Problem [Broken link]
George Reese, Buffon's Needle, An Analysis and Simulation
Shodor Education Foundation, Inc., Buffon's needle
Washington and Lee University, Problem 18: Buffon's Needle Again [Broken link]
Eric Weisstein's World of Mathematics, Buffon's needle problem
Eric Weisstein's World of Mathematics, BuffonLaplace needle problem
Eric Weisstein's World of Mathematics, Generalized Diameter


FORMULA

Equals sinc(Pi/6).  Peter Luschny, Oct 04 2019


EXAMPLE

3/Pi = 0.95492965855137201461330258023508617220675787444273869248600...


MATHEMATICA

RealDigits[ N[ 3/Pi, 111]][[1]]


CROSSREFS

Cf. A000796 (Pi), A060294 (2/Pi).
Sequence in context: A110894 A198933 A259148 * A199792 A193960 A195696
Adjacent sequences: A089488 A089489 A089490 * A089492 A089493 A089494


KEYWORD

cons,nonn


AUTHOR

Robert G. Wilson v, Nov 04 2003


STATUS

approved



