A249456 Decimal expansion of a constant appearing in the expression of the asymptotic expected volume V(d) of the convex hull of uniformly selected n(d) points in the interior of a d-dimensional unit cube.

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

Offset: 1

Author

Jean-François Alcover, Oct 29 2014

Keywords

• nonn
• cons
• easy

Examples

			2.139690947412859860505302263852352444323146956...
		

Links

• Steven R. Finch, Convex Lattice Polygons, December 18, 2003. [Cached copy, with permission of the author]

Crossrefs

Cf. A249455.

Programs

Mathematica

k = Exp[Log[2*Pi] - EulerGamma - 1/2]; RealDigits[k, 10, 103] // First

Formula

k = exp(log(2*Pi) - gamma - 1/2).

Lim_{d -> infinity} V(d) =

0 if n(d) <= (k - epsilon)^d

1 if n(d) >= (k + epsilon)^d