18 Sep
2020
18 Sep
'20
11:01 a.m.
The ultimate test is to see whichever definition leads to more interesting identities. The original Gauss AGM of course has many. For now I haven't seen any unexpected properties, so I don't know which is more "natural / simple / straightforward", maybe yours. Maybe neither, ha ha. It seems like your convergence proof also applies to the iteration I suggested, but I did not slow down to work out all the details. --Brad On Fri, Sep 18, 2020 at 11:19 AM M F Hasler <mhasler@dsi972.fr> wrote:
a = (a+b+c)/3 b = [( a*b + b*c + c*d )/3 ]^(1/2) c = (a*b*c)^(1/3)
I find the above one the most appealing (natural / simple / straightforward) one, though. It gives AGM(1,2,3) = 1.9099262335408153...
- Maximilian