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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 (list; constant; graph; refs; listen; history; text; internal format)
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 Buffon-Laplace 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. 135-138.

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, Buffon-Laplace 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

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)