A249523 Decimal expansion of rho(a,b), the cross-correlation coefficient of two sides of a random Gaussian triangle in three dimensions.

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

Offset: 0

Author

Jean-François Alcover, Oct 31 2014

Keywords

• nonn
• cons
• easy

Comments

Coordinates are independent normally distributed random variables with mean 0 and variance 1.

Examples

			0.237051025209600286585569504676408571940176916236978...
		

Links

• Steven R. Finch, Random Triangles, January 21, 2010. [Cached copy, with permission of the author]
• Eric Weisstein's MathWorld, Gaussian Triangle Picking

Crossrefs

Cf. A102519, A102520, A102556, A102557, A102558, A102559, A249491, A249492.

Programs

Mathematica

rho = (-8 + 3*Sqrt[3] + Pi)/(-8 + 3*Pi); RealDigits[rho, 10, 103] // First

PARI

(sqrt(27)+Pi-8)/(3*Pi-8) \\ Charles R Greathouse IV, Apr 20 2016

Formula

rho = (-8 + 3*sqrt(3) + Pi)/(-8 + 3*Pi).