Arithmetic-Geometric Mean -- from Wolfram MathWorld
The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = sqrt(a_nb_n) (2) until a_n=b_n to the desired precision....