A086201 -id:A086201 - cp's OEIS frontend

A087197 Decimal expansion of 1/sqrt(Pi).

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

Offset: 0

Sven Simon, Aug 24 2003

Radius of a circle with area 1.

Expectation of the maximum of a size 2 sample from a normal (0,1) distribution. - Jean-François Alcover, Jun 05 2014

			0.56418958354775628694...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.16 Extreme value constants, p. 365.

G. C. Greubel, Table of n, a(n) for n = 0..5000
Eric Weisstein's World of Mathematics, Inverse Erf
Index entries for transcendental numbers

Cf. A086201, A087198, A087199.

RealDigits[1/Sqrt[Pi], 10, 50][[1]] (* G. C. Greubel, Jan 09 2017 *)

Pi^-.5 \\ Charles R Greathouse IV, Nov 13 2015

Equals lim_{n -> infinity} Catalan(n)/(4^n*n^(-3/2)). - Jean-François Alcover, May 23 2013

Equals Sum_{k>=1} k/(2^k * Gamma(k+3/2)). - Amiram Eldar, May 27 2021

A132696 Decimal expansion of 6/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 26 2007, Nov 02 2007

6/Pi = Volume of the cuboid (If L1>L2>L3) / Volume of the inscribed ellipsoid.
6/Pi = Volume of the cuboid (If L1>(L2=L3)) / Volume of the inscribed spheroid.
6/Pi = Volume of the regular hexahedron (or cube) / Volume of the inscribed Sphere.
6/Pi = 1 / Arc of 30 degrees.
6/Pi = Volume of the cuboid (If L1<(L2=L3)) / Volume of the inscribed spheroid.
6/Pi = Surface area of the regular hexahedron (or cube) / surface area of the inscribed sphere.

			1.90985931710274402922660516047... .

Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201, A059956.

RealDigits[N[6/Pi, 200]] (* Erich Friedman, Mar 22 2008 *)

6/Pi \\ Charles R Greathouse IV, Dec 31 2011

Equals Product_{k>=1} (2k+1)^3 / ( (2k)^2*(2k+3) ). - Federico Provvedi, Nov 09 2024

More terms from Erich Friedman, Mar 22 2008

A132702 Decimal expansion of 12/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 26 2007

From Bernard Schott, Apr 17 2022: (Start)
For any triangle ABC, (see Crux Mathematicorum):
(b+c)/A + (c+a)/B + (a+b)/C >= (12/Pi) * s,
b*c/(A*(s-a)) + c*a/(B*(s-b)) + a*b/(C*(s-c)) >= (12/Pi) * s,
where (A,B,C) are the angles (measured in radians), (a,b,c) the side lengths of this triangle and s the semiperimeter.
Equality stands iff triangle ABC is equilateral. (End)

			3.819718634...

S. Arslanagić and D. M. Milošević, Problem 1827, Crux Mathematicorum, Vol. 22, No. 1 (1996), p. 36.
Index entries for transcendental numbers.

Cf. A049541, A060294, A089491, A088538, A086201.

Digits:=100; evalf(12/Pi); # Wesley Ivan Hurt, Mar 26 2014

RealDigits[N[12/Pi,6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2009 *)

12/Pi \\ Charles R Greathouse IV, Dec 31 2011

Equals 2*A132696 = 4*A089491 = 6*A060294. -R. J. Mathar, Jul 29 2024

More terms from Vladimir Joseph Stephan Orlovsky, Jun 19 2009

A132699 Decimal expansion of 9/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 26 2007

9/Pi = 2.864788975654...

Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201.

Digits:=100; evalf(9/Pi); # Wesley Ivan Hurt, Mar 26 2014

RealDigits[N[9/Pi,6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2009 *)

9/Pi \\ Charles R Greathouse IV, Dec 31 2011

More terms from Vladimir Joseph Stephan Orlovsky, Jun 19 2009

A132701 Decimal expansion of 11/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 26 2007

			3.501408748021697...

Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201.

Digits:=100; evalf(11/Pi); # Wesley Ivan Hurt, Mar 26 2014

RealDigits[N[11/Pi,6! ]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2009 *)

11/Pi \\ Charles R Greathouse IV, Dec 31 2011

More terms from Vladimir Joseph Stephan Orlovsky, Jun 19 2009

A087198 Decimal expansion of 1/(2*sqrt(Pi)).

Original entry on oeis.org

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

Offset: 0

Sven Simon, Aug 24 2003

Radius of a sphere with surface area 1.

According to Fouad (2004), to simulate the distance of a sound source under free field conditions, one can multiply "the waveform directly by a gain factor that is the square root of the intensity," which can be computed with the formula D = sqrt(1/(4 * Pi * d^2)) = 1/(3.55 * d), where d is the distance between the sound source and the listener and 3.55 is approximately 10(sqrt(Pi)/5) (A019707) (equation 15 in the chapter), though "in practice we usually drop the constant multiplier" (4 * Pi). If the distance is one unit, then D works out to this number. - Alonso del Arte, Jun 10 2012

			0.28209479177387814347...

Hesham Fouad, "Spatialization with Stereo Loudspeakers: Understanding Balance, Panning and Distance Attenuation" in Audio Anecdotes II: Tools, Tips, and Techniques for Digital Audio, K. Greenebaum & R. Barzel, eds. Wellesley, Massachusetts: A K Peters (2004): 150 - 153

G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for transcendental numbers

Cf. A086201, A087197, A087199.

RealDigits[Sqrt[1/(4Pi)], 10, 100][[1]] (* Alonso del Arte, Jun 10 2012 *)

sqrt(1/(4*Pi)) \\ G. C. Greubel, Jan 09 2017

1/(2 * sqrt(Pi)) = sqrt(1/(4 * Pi)).

A093070 Decimal expansion of 128/(45*Pi).

Original entry on oeis.org

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

Offset: 0

Eric W. Weisstein, Mar 17 2004

Average length of a line picked at random in a unit disk.

			0.90541478736722679904076096496363725957381487354570...

Eric Weisstein's World of Mathematics, Disk Line Picking.
Eric Weisstein's World of Mathematics, Circular Sector Line Picking.
Index entries for transcendental numbers

Cf. A000796, A086201.

RealDigits[128/(45*Pi), 10, 100][[1]] (* Amiram Eldar, Apr 14 2022 *)

128/Pi/45 \\ Charles R Greathouse IV, Sep 28 2022

Equals (256*A086201)/45. - Kritsada Moomuang, Sep 19 2020

A087199 Decimal expansion of (3/(4*Pi))^(1/3).

Original entry on oeis.org

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

Offset: 0

Sven Simon, Aug 24 2003

Radius of a sphere of volume 1.

			0.62035049089940001666800681204777816735078620018600162009895688991314690606003....

Index entries for transcendental numbers

Cf. A086201, A087197, A087198.

RealDigits[(3/(4 Pi))^(1/3), 10, 111][[1]] (* Robert G. Wilson v, Sep 29 2014 *)

A132698 Decimal expansion of 8/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 26 2007

			2.5464790894703253723021402139602297925513543318473031799626775049423487621476....

Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201.

Digits:=100; evalf(8/Pi); # Wesley Ivan Hurt, Mar 26 2014

RealDigits[N[8/Pi,6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 02 2009 *)

8/Pi \\ Charles R Greathouse IV, Oct 01 2022

More terms from Vladimir Joseph Stephan Orlovsky, Dec 02 2009

A132714 Decimal expansion of 24/Pi.

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Aug 31 2007

			=7.639437268410976116906420641880689377654062995541909539888032514827...

G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for transcendental numbers

Cf. A049541, A060294, A089491, A088538, A086201, A132696 to A132699, A132701, A132702.

RealDigits[N[24/Pi,6! ]] (* Vladimir Joseph Stephan Orlovsky, Dec 03 2009 *)

PARI
```
24/Pi \\ G. C. Greubel, Feb 20 2017
```

24/Pi = Sum_{k>=0} ( (30*k+7)*C(2*k,k)^2*(Hypergeometric2F1[1/2 - k/2, -k/2, 1, 64])/(-256)^k ). - Alexander R. Povolotsky, Dec 20 2012

Another version of this identity is: Sum[(30*k+7) * Binomial[2k,k]^2 * (Sum[Binomial[k-m,m] * Binomial[k,m] * 16^m, {m,0,k/2}])/(256)^k, {k,0,infinity}]. - Alexander R. Povolotsky, Jan 25 2013

More terms from Vladimir Joseph Stephan Orlovsky, Dec 03 2009

cp's OEIS Frontend

A087197 Decimal expansion of 1/sqrt(Pi).

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A132696 Decimal expansion of 6/Pi.

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A132702 Decimal expansion of 12/Pi.

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A132699 Decimal expansion of 9/Pi.

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A132701 Decimal expansion of 11/Pi.

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A087198 Decimal expansion of 1/(2*sqrt(Pi)).

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A093070 Decimal expansion of 128/(45*Pi).

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