

A019694


Decimal expansion of 2*Pi/5.


29



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
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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
Iff n is + 1, 2, 3, 4 or 6, then 2*cos(2*Pi/n) is an integer. This formula plays a role in the short proof of the Crystallographic Restriction Theorem (see A217290). For n = 5, 2*cos(2*Pi/5) = 1/Golden Ratio = 0.6180339887..., associated with quasicrystals and 5fold rotational symmetry.  Raphie Frank, Dec 21 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


LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..1000
NIST, magnetic constant mu_0.
Nobelprize.org, The Discovery of Quasicrystals (PDF).
Wikipedia, Crystallographic Restriction Theorem.
Index entries for transcendental numbers


FORMULA

Equals Sum_{k>=1} sin(Pi*k/5)/k.  Amiram Eldar, Aug 12 2020


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.
Sequence in context: A272207 A155947 A008294 * A233588 A113975 A035585
Adjacent sequences: A019691 A019692 A019693 * A019695 A019696 A019697


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane


STATUS

approved



