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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).
0
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.
FORMULA
1-35/(12*Pi^2).
EXAMPLE
0.70447988104318149995535...
MATHEMATICA
RealDigits[1 - 35/(12*Pi^2), 10, 103] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved