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

Author

Jean-François Alcover, May 22 2014

Keywords

• nonn
• cons

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

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

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).