A019679 Decimal expansion of Pi/12.

2, 6, 1, 7, 9, 9, 3, 8, 7, 7, 9, 9, 1, 4, 9, 4, 3, 6, 5, 3, 8, 5, 5, 3, 6, 1, 5, 2, 7, 3, 2, 9, 1, 9, 0, 7, 0, 1, 6, 4, 3, 0, 7, 8, 3, 2, 8, 1, 2, 5, 8, 8, 1, 8, 4, 1, 4, 5, 7, 8, 7, 1, 6, 0, 2, 5, 6, 5, 1, 3, 6, 7, 1, 9, 0, 5, 1, 7, 4, 1, 6, 5, 5, 2, 3, 3, 6, 2, 3, 5, 4, 4, 5, 1, 7, 6, 4, 2, 2

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Equals cone's volume (radius = 1/2, height = 1) and semi-sphere's volume (radius = 1/2). - Eric Desbiaux, Dec 08 2008

Decimal expansion of least x > 0 having cos(4x) = (cos 3x)^2. See A197476. - Clark Kimberling, Oct 15 2011

Multiplied by 10, decimal expansion of 5*Pi/6. - Alonso del Arte, Aug 19 2013

Volume between a cylinder and the inscribed sphere of diameter 1. - Omar E. Pol, Sep 25 2013

Examples

			Pi/12 = 0.2617993877991494365385536152732919070164307...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.4, p. 492.

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for transcendental numbers.

Crossrefs

Cf. A000796, A003881, A019669, A019670, A019675, A019683, A244978.

Programs

Mathematica

RealDigits[N[Pi/12, 6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)
RealDigits[Pi/12,10,120][[1]] (* Harvey P. Dale, Jan 12 2024 *)

PARI

Pi/12 \\ Charles R Greathouse IV, Sep 28 2022

Formula

A003881 - A019673. - Omar E. Pol, Sep 25 2013

Equals Integral_{x = 0..1} x^2*sqrt(1 - x^6) dx. - Peter Bala, Oct 27 2019

Equals Sum_{k>=0} binomial(2*k,k)/((2*k+1)*4^(2*k+1)). - Amiram Eldar, May 30 2021

Constant divided by 10 = Pi/120 = 0.0261799387... = Sum_{n = -oo..oo} 1/((4*n+1)*(4*n+2)*(4*n+3)*(4*n+5)*(4*n+6)*(4*n+7)) (using the Eisenstein summation convention Sum_{n = -oo..oo} = lim_{N -> oo} Sum_{n = -N..N}). Note that 22/7 - Pi = 240*Sum_{n >= 1} 1/((4*n+1)*(4*n+2)*(4*n+3)*(4*n+5)*(4*n+6)*(4*n+7)). - Peter Bala, Nov 28 2021