Search: id:A060294
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%I A060294
%S A060294 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,
%T A060294 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,
%U A060294 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
%N A060294 Decimal expansion of Buffon's constant 2/Pi.
%C A060294 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
%C A060294 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
%C A060294 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
%D A060294 G. Buffon, Essai d'arithmetique morale. Supplement a l'Histoire Naturelle, 
               Vol. 4, 1777.
%D A060294 S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and 
               its Applications, vol. 94, Cambridge University Press, p. 141
%D A060294 R. Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan, 
               1991.
%D A060294 D. A. Klain and G.-C. Rota, Introduction to Geometric Probability, Cambridge, 
               1997, see Chap. 1.
%D A060294 L. A. Santalo, Integral Geometry and Geometric Probability, Addison-Wesley, 
               1976.
%H A060294 Harry J. Smith, <a href="b060294.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A060294 Boris Gourevitch, <a href="http://membres.lycos.fr/bgourevitch/">Tout 
               l'univers de Pi</a>
%H A060294 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BuffonsNeedleProblem.html">Buffon's needle problem</a>
%H A060294 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               MagicGeometricConstants.html">Magic Geometric Constants</a>
%H A060294 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PrimeProducts.html">Prime Products</a>
%F A060294 2/Pi = 1 - 5(1/2)^3 + 9(1*3/2*4)^3 - 13(1*3*5/2*4*6)...
%e A060294 2/Pi = 0.6366197723675813430755350534900574481378385829618257949906...
%t A060294 RealDigits[ N[ 2/Pi, 111]][[1]]
%o A060294 (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]
%Y A060294 Cf. A000796 (Pi).
%Y A060294 Cf. A088538.
%Y A060294 Cf. A154956. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Jan 25 2009]
%Y A060294 Sequence in context: A069938 A043296 A137245 this_sequence A021615 A078888 
               A021161
%Y A060294 Adjacent sequences: A060291 A060292 A060293 this_sequence A060295 A060296 
               A060297
%K A060294 cons,nonn
%O A060294 0,1
%A A060294 Jason Earls (zevi_35711(AT)yahoo.com), Mar 28 2001

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