(Just playing around with the standard definition of AGM, I see that it tends to converge to 15 decimal places almost always within 5 or 6 iterations -- so it already has impressive convergence.) Define an equivalence relation via (x,y) ~ (x',y') whenever AGM(x,y) = AGM(x',y'). Then what do the equivalence classes look like as subsets of (0,oo)^2 ? They're most likely all curves; what are their equations? --Dan Also -- and this is probably well-known -- it seems that the "weighted AGM": a(n+1) = p*a(n) + q*g(n) g(n+1) = a(n)^p * g(n)^q where 0 < p < 1, p+q= 1, always converges for positive a(0),g(0) as well. _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele