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Search: id:A060294
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| A060294 |
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Decimal expansion of Buffon's constant 2/Pi. |
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+0
27
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| 6, 3, 6, 6, 1, 9, 7, 7, 2, 3, 6, 7, 5, 8, 1, 3, 4, 3, 0, 7, 5, 5, 3, 5, 0, 5, 3, 4, 9, 0, 0, 5, 7, 4, 4, 8, 1, 3, 7, 8, 3, 8, 5, 8, 2, 9, 6, 1, 8, 2, 5, 7, 9, 4, 9, 9, 0, 6, 6, 9, 3, 7, 6, 2, 3, 5, 5, 8, 7, 1, 9, 0, 5, 3, 6, 9, 0, 6, 1, 4, 0, 3, 6, 0, 4, 5, 5, 2, 1, 1, 0, 6, 5, 0, 1, 2, 3, 4, 3, 8, 2, 4, 2, 9, 1
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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The probability P(l,d) that a needle of length l will land on a line, given a floor with equally spaced parallel lines at a distance d (>=l) apart, is (2/Pi)*(l/d). - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 14 2002
Lim n-->infinity z(n)/log(n)=2/Pi, where z(n) is the expected number of real zeros of a random polynomial of degree n with real coefficients chosen from a standard Gaussian distribution (cf. Finch reference). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 02 2003
Also the ratio of the average chord length when two points are chosen at random on a circle of radius r to the maximum possible chord length (i.e. diameter) = A088538*r / 2*r = 2/Pi. Is there a (direct or obvious) relationship between this fact and that 2/Pi is the "magic geometric constant" for a circle (see MathWorld link)? - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 22 2006
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REFERENCES
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G. Buffon, Essai d'arithmetique morale. Supplement a l'Histoire Naturelle, Vol. 4, 1777.
S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, p. 141
R. Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan, 1991.
D. A. Klain and G.-C. Rota, Introduction to Geometric Probability, Cambridge, 1997, see Chap. 1.
L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 1976.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
Boris Gourevitch, Tout l'univers de Pi
Eric Weisstein's World of Mathematics, Buffon's needle problem
Eric Weisstein's World of Mathematics, Magic Geometric Constants
Eric Weisstein's World of Mathematics, Prime Products
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FORMULA
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2/Pi = 1 - 5(1/2)^3 + 9(1*3/2*4)^3 - 13(1*3*5/2*4*6)...
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EXAMPLE
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2/Pi = 0.6366197723675813430755350534900574481378385829618257949906...
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MATHEMATICA
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RealDigits[ N[ 2/Pi, 111]][[1]]
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PROGRAM
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(PARI) { default(realprecision, 20080); x=20/Pi; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b060294.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 03 2009]
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CROSSREFS
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Cf. A000796 (Pi).
Cf. A088538.
Cf. A154956. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Jan 25 2009]
Sequence in context: A069938 A043296 A137245 this_sequence A021615 A078888 A021161
Adjacent sequences: A060291 A060292 A060293 this_sequence A060295 A060296 A060297
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KEYWORD
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cons,nonn
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AUTHOR
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Jason Earls (zevi_35711(AT)yahoo.com), Mar 28 2001
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