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.

Showing 1-2 of 2 results.

A051051 Denominators of the probability that the convex hull of n+2 randomly chosen points in the unit ball B^n has n+1 vertices (with factor of Pi^n dropped for n even).

Original entry on oeis.org

1, 12, 143, 648000, 12964479, 1721036800000, 2077805148460987, 5041895218133760000000, 14154229032767142723739127, 51951524164830314976613655528865792
Offset: 0

Views

Author

Eric W. Weisstein

Keywords

Links

Crossrefs

Cf. A051050.

A242780 Decimal expansion of the maximum probability that the convex hull of four points, chosen at random inside a convex planar region, is a quadrilateral (Sylvester's four-point problem).

Original entry on oeis.org

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

Views

Author

Jean-François Alcover, May 22 2014

Keywords

Comments

It is proved that this maximum probability is achieved when the region is an ellipse (or a disk). [after Steven Finch]

Examples

			0.70447988104318149995535...

References

  • Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.18, p. 533.

Links

Crossrefs

Cf. A004677, A004824, A004936, A005017, A051050, A051051.

Programs

  • Mathematica
    RealDigits[1 - 35/(12*Pi^2), 10, 103] // First
  • PARI
    1 - 35/(12*Pi^2) \\ Stefano Spezia, Dec 26 2024

Formula

Equals 1 - 35/(12*Pi^2).
Showing 1-2 of 2 results.

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

Content is available under The OEIS End-User License Agreement.