A019694 Decimal expansion of 2*Pi/5.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

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

Examples

			1.2566370614359172953850573533118....
mu_0 = 12.566370614359172953850573533118... 10^-7 N/A^2. - _Stanislav Sykora_, Jun 16 2012
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 1..1000
• NIST, magnetic constant mu_0.
• Nobelprize.org, The Discovery of Quasicrystals (PDF).
• Eric Weisstein's World of Mathematics, Witch of Agnesi.
• Wikipedia, Crystallographic Restriction Theorem.
• Index entries for sequences related to curves.
• Index entries for transcendental numbers.

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).

Programs

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 *)

PARI

2*Pi/5 \\ G. C. Greubel, Sep 11 2017

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