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Search: id:A089491
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| A089491 |
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Decimal expansion of Buffon's constant 3/Pi. |
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+0
23
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| 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; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (rshepherd2(AT)hotmail.com), Jan 11 2006
Related grid problems are discussed in the Weisstein/MathWorld Buffon-Laplace Needle Problem link. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jan 11 2006
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REFERENCES
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Joe Portney, Portney's Ponderables, Litton Systems, Inc., Appendix 2, 'Buffon's Needle' by Lawrence R. Weill, 200, pgs. 135-8.
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LINKS
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Harry Khamis, Buffon's Needle Problem
Kevin Peterson, A Problem in Geometric Probability: Buffon's Needle Problem
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
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
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EXAMPLE
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3/Pi = 0.95492965855137201461330258023508617220675787444273869248600...
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MATHEMATICA
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RealDigits[ N[ 3/Pi, 111]][[1]]
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CROSSREFS
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Cf. A000796 (Pi), A060294 (2/Pi).
Sequence in context: A104139 A071831 A110894 this_sequence A155534 A154683 A019882
Adjacent sequences: A089488 A089489 A089490 this_sequence A089492 A089493 A089494
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KEYWORD
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cons,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2003
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