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A019694 Decimal expansion of 2*Pi/5. 33

%I #103 Aug 05 2023 13:18:20

%S 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,

%T 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,

%U 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

%N Decimal expansion of 2*Pi/5.

%C 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]

%C Regarding these, see A003678 for general context notes, references and links. - _Stanislav Sykora_, Jun 16 2012

%C 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

%C 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

%H Ivan Panchenko, <a href="/A019694/b019694.txt">Table of n, a(n) for n = 1..1000</a>

%H NIST, <a href="http://physics.nist.gov/cgi-bin/cuu/Value?mu0">magnetic constant mu_0</a>.

%H Nobelprize.org, <a href="https://www.nobelprize.org/uploads/2018/06/advanced-chemistryprize2011.pdf">The Discovery of Quasicrystals (PDF)</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WitchofAgnesi.html">Witch of Agnesi</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Crystallographic_restriction_theorem">Crystallographic Restriction Theorem</a>.

%H <a href="/index/Cu#curves">Index entries for sequences related to curves</a>.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%F Equals Sum_{k>=1} sin(Pi*k/5)/k. - _Amiram Eldar_, Aug 12 2020

%F Equals -zeta(3/2)/(10*zeta(-1/2)). - _Mats Granvik_, May 28 2022

%e 1.2566370614359172953850573533118....

%e mu_0 = 12.566370614359172953850573533118... 10^-7 N/A^2. - _Stanislav Sykora_, Jun 16 2012

%p Digits:=100: evalf(2*Pi/5); # _Wesley Ivan Hurt_, Jan 07 2017

%t RealDigits[ 2*Pi/5, 10, 111][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Dec 02 2009 and modified by _Robert G. Wilson v_ *)

%o (PARI) 2*Pi/5 \\ _G. C. Greubel_, Sep 11 2017

%Y Other assigned constants: A003678, A072915, A081799, A182999, A213610, A213611, A213612, A213613, A213614.

%Y Cf. A093828 (astroid), A180434 (loop of strophoid), A197723 (cardioid), A336266 (double egg), A336308 (ovoid).

%K nonn,cons

%O 1,2

%A _N. J. A. Sloane_

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