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A019692
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Decimal expansion of 2*Pi.
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27
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6, 2, 8, 3, 1, 8, 5, 3, 0, 7, 1, 7, 9, 5, 8, 6, 4, 7, 6, 9, 2, 5, 2, 8, 6, 7, 6, 6, 5, 5, 9, 0, 0, 5, 7, 6, 8, 3, 9, 4, 3, 3, 8, 7, 9, 8, 7, 5, 0, 2, 1, 1, 6, 4, 1, 9, 4, 9, 8, 8, 9, 1, 8, 4, 6, 1, 5, 6, 3, 2, 8, 1, 2, 5, 7, 2, 4, 1, 7, 9, 9, 7, 2, 5, 6, 0, 6, 9, 6, 5, 0, 6, 8, 4, 2, 3, 4, 1, 3
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OFFSET
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1,1
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COMMENTS
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pi/5 or 2*pi/10 is the expected surface area containing completely a Brownian curve (trajectory) on plane. - Lekraj Beedassy, Jul 28 2005
Bob Palais considers this a more fundamental constant that pi. As noted in the last page of the pdf, he suggests calling the alternate constant 2 pi = 6.283... '1 turn', so that 90 degrees is 'a quarter turn', just as we would say in natural language. The main point is that the historical choice of the value of pi obscures the benefit of radian measure. It is easy to see that 1/4 turn is more natural than 90 degrees, but pi/2 seems almost as arbitrary. It is apparent that we can't eliminate pi but it is to be aware of its pitfalls, and introduce an alternative for those who might wish to use one. - Jonathan Vos Post, Sep 10 2010
The Persian mathematician Jamshid al-Kashi seems to have been the first to use the circumference divided by the radius as the circle constant. In Treatise on the Circumference published 1424 he calculated the circumference of a unit circle to 9 sexagesimal places. [Comments from Peter Harremoës, John W. Nicholson, Aug 2, 2012]
"Proponents of a new mathematical constant tau (τ), equal to two times π, have argued that a constant based on the ratio of a circle's circumference to its radius rather than to its diameter would be more natural and would simplify many formulae" (from Wikipedia). - Jonathan Sondow, Aug 15 2012.
The constant 2*Pi appears in the formula for the period T of a simple gravity pendulum. For small angles this period is given by Christiaan Huygens’s law, i.e. T = 2*Pi*sqrt(L/g), see for more information A223067. - Johannes W. Meijer, Mar 14 2013
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REFERENCES
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Bob Palais, "Pi is wrong!", The Mathematical Intelligencer Volume 23, Number 3, 2001, pp. 7-8.
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..20000
C. Garban & J. A. T. Ferreras, The expected area of the filled planar Brownian loop is pi/5
Peter Harremoës, web page about "Al-Kashi’s constant τ"
Michael Hartl, The Tau Manifesto
Bob Palais, Web page about "Pi is wrong!"
Wikipedia, Tau (2π)
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EXAMPLE
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6.283185307179586476925286766559005768394338798750211641949889184615632...
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MATHEMATICA
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RealDigits[N[Pi/5, 6! ]] [Vladimir Joseph Stephan Orlovsky, Dec 02 2009]
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PROG
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(PARI) { default(realprecision, 20080); x=2*Pi; for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019692.txt", n, " ", d)); } [Harry J. Smith, May 31 2009]
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CROSSREFS
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Cf. A058291 Continued fraction.
Sequence in context: A021090 A177889 A086744 * A031259 A059629 A082577
Adjacent sequences: A019689 A019690 A019691 * A019693 A019694 A019695
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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