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A019694 Decimal expansion of 2*Pi/5. 33
1, 2, 5, 6, 6, 3, 7, 0, 6, 1, 4, 3, 5, 9, 1, 7, 2, 9, 5, 3, 8, 5, 0, 5, 7, 3, 5, 3, 3, 1, 1, 8, 0, 1, 1, 5, 3, 6, 7, 8, 8, 6, 7, 7, 5, 9, 7, 5, 0, 0, 4, 2, 3, 2, 8, 3, 8, 9, 9, 7, 7, 8, 3, 6, 9, 2, 3, 1, 2, 6, 5, 6, 2, 5, 1, 4, 4, 8, 3, 5, 9, 9, 4, 5, 1, 2, 1, 3, 9, 3, 0, 1, 3, 6, 8, 4, 6, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also, with proper offset, decimal expansion of the magnetic permeability of vacuum in SI units, mu_0 = 4*Pi*10^-7 N A^-2, an assigned metrological constant. [This exact expression for mu_0 was valid until the 2019 SI redefinition. In the New SI, mu_0 is numerically very close to that value but is determined only up to a certain error. - Andrey Zabolotskiy, May 22 2019]
Regarding these, see A003678 for general context notes, references and links. - Stanislav Sykora, Jun 16 2012
With offset 2 this is also the decimal expansion of 4*Pi, the surface area of a sphere whose diameter equals the square root of 4, hence its radius is 1. More generally x*Pi is also the surface area of a sphere whose diameter equals the square root of x. - Omar E. Pol, Jan 18 2013, Oct 05 2013, Dec 22 2013
4*Pi is also the area of the domain bounded by the witch of Agnesi whose Cartesian equation is y = 8 / (x^2 + 4) and its asymptote. More generally (4*Pi) * a^2 is the area of the domain bounded by the witch of Agnesi whose Cartesian equation is y = (8*a^3) / (x^2 + 4*a^2) and its asymptote (Eric Weisstein's link, formula 6). - Bernard Schott, Jun 28 2023
LINKS
Eric Weisstein's World of Mathematics, Witch of Agnesi.
FORMULA
Equals Sum_{k>=1} sin(Pi*k/5)/k. - Amiram Eldar, Aug 12 2020
Equals -zeta(3/2)/(10*zeta(-1/2)). - Mats Granvik, May 28 2022
EXAMPLE
1.2566370614359172953850573533118....
mu_0 = 12.566370614359172953850573533118... 10^-7 N/A^2. - Stanislav Sykora, Jun 16 2012
MAPLE
Digits:=100: evalf(2*Pi/5); # Wesley Ivan Hurt, Jan 07 2017
MATHEMATICA
RealDigits[ 2*Pi/5, 10, 111][[1]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 and modified by Robert G. Wilson v *)
PROG
(PARI) 2*Pi/5 \\ G. C. Greubel, Sep 11 2017
CROSSREFS
Other assigned constants: A003678, A072915, A081799, A182999, A213610, A213611, A213612, A213613, A213614.
Cf. A093828 (astroid), A180434 (loop of strophoid), A197723 (cardioid), A336266 (double egg), A336308 (ovoid).
Sequence in context: A272207 A155947 A008294 * A233588 A113975 A035585
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)