A249492 Decimal expansion of rho(a,b), the cross-correlation coefficient of two sides of a random Gaussian triangle (in two dimensions).

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

Offset: 0

Author

Jean-François Alcover, Oct 30 2014

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			0.23255934654317823447309035975033389931043501543502...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Steven R. Finch, Random Triangles, January 21, 2010. [Cached copy, with permission of the author]
• Eric Weisstein MathWorld, Gaussian Triangle Picking

Crossrefs

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

Programs

Maple

Re(evalf((4*EllipticE(1/2) - sqrt(3)*EllipticK(I/sqrt(3)) - Pi)/(4 - Pi), 120)); # Vaclav Kotesovec, Apr 22 2015

Mathematica

p = 4*EllipticE[1/4] - Sqrt[3]*EllipticK[-1/3]; rho = (p - Pi)/(4 - Pi); RealDigits[rho, 10, 103] // First
RealDigits[(3 EllipticE[8/9] - Pi)/(4 - Pi), 10, 103][[1]] (* Jan Mangaldan, Nov 26 2020 *)

Formula

rho = (p - Pi)/(4 - Pi), where p is A249491, the expected value of the product of two sides.