login
A249523
Decimal expansion of rho(a,b), the cross-correlation coefficient of two sides of a random Gaussian triangle in three dimensions.
0
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
0,1
COMMENTS
Coordinates are independent normally distributed random variables with mean 0 and variance 1.
LINKS
Steven R. Finch, Random Triangles, January 21, 2010. [Cached copy, with permission of the author]
Eric Weisstein's MathWorld, Gaussian Triangle Picking
FORMULA
rho = (-8 + 3*sqrt(3) + Pi)/(-8 + 3*Pi).
EXAMPLE
0.237051025209600286585569504676408571940176916236978...
MATHEMATICA
rho = (-8 + 3*Sqrt[3] + Pi)/(-8 + 3*Pi); RealDigits[rho, 10, 103] // First
PROG
(PARI) (sqrt(27)+Pi-8)/(3*Pi-8) \\ Charles R Greathouse IV, Apr 20 2016
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved