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).

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

0,1

Comments

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

References

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

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's MathWorld, Sylvester's Four-Point Problem

Formula

1-35/(12*Pi^2).

Example

0.70447988104318149995535...

Mathematica

RealDigits[1 - 35/(12*Pi^2), 10, 103] // First

Crossrefs

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

Sequence in context: A070513 A065463 A319739 * A324997 A011392 A177156

Adjacent sequences: A242777 A242778 A242779 * A242781 A242782 A242783

Keyword

nonn,cons

Author

Jean-François Alcover, May 22 2014

Status

approved