cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A265729 Decimal expansion of 32*Pi.

Original entry on oeis.org

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

Views

Author

Eric W. Weisstein and Robert G. Wilson v, Dec 14 2015

Keywords

Comments

"The integral corresponds to integration over a spherical cone with opening angle Pi/2 and radius 4. However, it is not clear what the integrand physically represents (it resembles computation of a moment of inertia, but that would give a factor (rho*sin(phi))^2 rather than the given rho*cos(phi))."

Examples

			100.53096491487338363080458826494409229430942078000338627119822695385012500...

References

  • The Jun 02 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007)

Links

Crossrefs

Cf. A000796, A019692, A122952, A019694, A019669, A228719, A228721, A228824, A229939, A061146.

Programs

  • Mathematica
    RealDigits[32 Pi, 10, 111][[1]] (* or *)
Integrate[\[Rho] Cos[\[Phi]] \[Rho]^2 Sin[\[Phi]], {\[Rho], 0, 4}, {\[Phi], 0, Pi/4}, {\[Theta], 0, 2 Pi}]
  • PARI
    32*Pi \\ Altug Alkan, Dec 14 2015

Formula

Equals Integral_{theta=0..2*Pi} Integral_{phi=0..Pi/4} Integral_{rho=0..4} (rho*cos(phi))*rho^2*sin(phi) d(rho) d(phi) d(theta).

A375741 Decimal expansion of 6*Pi/(3*sqrt(3) + 8*Pi).

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Aug 26 2024

Keywords

Comments

This constant expresses the expected proportion of individuals that belong to reciprocal nearest-neighbor relationship pairs in a population of random patterns over a plane.

Examples

			0.62150489688743159140596781880802827312707885...

References

  • E. C. Pielou, An Introduction to Mathematical Ecology, John Wiley & Sons, Inc. 1969. See pp. 121-122.

Links

Crossrefs

Cf. A000796, A010482, A010527, A019692, A019699, A228719, A228824.

Programs

  • Mathematica
    RealDigits[6Pi/(3Sqrt[3]+8Pi),10,100][[1]]

Formula

Equals Integral_{x=0..oo} 2*Pi*x*exp(-x^2*(sqrt(3)/2+4*Pi/3)) dx. [Pielou, 1969]
Previous Showing 11-12 of 12 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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