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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A336199 Decimal expansion of the distance between the centers of two unit-radius spheres such that the volume of intersection is equal to the sum of volumes of the two nonoverlapping parts.

Original entry on oeis.org

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

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Author

Amiram Eldar, Jul 11 2020

Keywords

Comments

Solution to the three-dimensional version of Mrs. Miniver's problem.
The intersection volume is equal to 2/3 of the volume of each sphere, i.e., 8*Pi/9.

Examples

			0.452147427578415981828610831183181263247509153259677...

Links

Crossrefs

Cf. A019673, A019699, A133749, A156546, A255899.

Programs

  • Mathematica
    RealDigits[4 * Sin[ArcCos[-1/3]/3 - Pi/6], 10, 100][[1]]

Formula

Equals 4 * sin(arccos(-1/3)/3 - Pi/6).
The smaller of the two positive roots of the equation x^3 - 12*x + 16/3 = 0.

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 21-22 of 22 results.

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

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