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 A019692 Decimal expansion of 2*Pi. 27

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of 2*Pi.

%C pi/5 or 2*pi/10 is the expected surface area containing completely a Brownian curve (trajectory) on plane. - _Lekraj Beedassy_, Jul 28 2005

%C 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

%C 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]

%C "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.

%C 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

%D Bob Palais, "Pi is wrong!", The Mathematical Intelligencer Volume 23, Number 3, 2001, pp. 7-8.

%H Harry J. Smith, <a href="/A019692/b019692.txt">Table of n, a(n) for n = 1..20000</a>

%H C. Garban & J. A. T. Ferreras, <a href="http://fr.arXiv.org/abs/math.PR/0504496">The expected area of the filled planar Brownian loop is pi/5</a>

%H Peter Harremoës, <a href="http://www.harremoes.dk/Peter/Undervis/Turnpage/Turnpage1.html"> web page about "Al-Kashi’s constant τ"</a>

%H Michael Hartl, <a href="http://tauday.com">The Tau Manifesto</a>

%H Bob Palais, <a href="http://www.math.utah.edu/~palais/pi.html">Web page about "Pi is wrong!"</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tau_(2π)#In_popular_culture">Tau (2π)</a>

%e 6.283185307179586476925286766559005768394338798750211641949889184615632...

%t RealDigits[N[Pi/5,6! ]] [_Vladimir Joseph Stephan Orlovsky_, Dec 02 2009]

%o (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]

%Y Cf. A058291 Continued fraction.

%K nonn,cons

%O 1,1

%A _N. J. A. Sloane_.

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