03/15/2011, 10:22 PM
if i understand this confusing thread well
x {0.5} x = x !
in fact x {y} x = x
at least following from
( quote )
In other words, for a {0.25} b, with a<b,
m1 of a and b = a + (b-a)*0.25 (0.25 of the way between a and b, judged arithmetically)
m2 of a and b = a * (b/a)^0.25 (0.25 of the way between a and b, judged geometrically)
Now plug m1 and m2 into a and b, and iterate until you get something stable (i.e. m1 = m2 to whatever degree of precision you need)
( end quote )
unless you guys started using different ideas since the time of the quote.
furthermore i think this has nothing to do with * tetration * and see it more like an idea inspired by Gauss Aritmetic-Geometric Mean.
If this was not my favorite forum and due to the lack of good math forums in general imho , i might not have read it in the first place ( OP was already unaware of Gauss AGM Mean ) although it might get intresting soon ...
i would be more carefull to associate this immediately with a new * slog *.
i think JmsNxn is a bit overenthousiastic.
maybe its me , but the only intresting thing i can see at the moment is :
does this ' new ' mean have a closed form similar to gauss his result ?
( i assume its analytic ?? for complex z_i : z1 {z2} z3 ? )
furthermore , i have no idea why JmsNxn thinks x {1.5} 2 = x {0.5} x
???
tommy1729
x {0.5} x = x !
in fact x {y} x = x
at least following from
( quote )
In other words, for a {0.25} b, with a<b,
m1 of a and b = a + (b-a)*0.25 (0.25 of the way between a and b, judged arithmetically)
m2 of a and b = a * (b/a)^0.25 (0.25 of the way between a and b, judged geometrically)
Now plug m1 and m2 into a and b, and iterate until you get something stable (i.e. m1 = m2 to whatever degree of precision you need)
( end quote )
unless you guys started using different ideas since the time of the quote.
furthermore i think this has nothing to do with * tetration * and see it more like an idea inspired by Gauss Aritmetic-Geometric Mean.
If this was not my favorite forum and due to the lack of good math forums in general imho , i might not have read it in the first place ( OP was already unaware of Gauss AGM Mean ) although it might get intresting soon ...
i would be more carefull to associate this immediately with a new * slog *.
i think JmsNxn is a bit overenthousiastic.
maybe its me , but the only intresting thing i can see at the moment is :
does this ' new ' mean have a closed form similar to gauss his result ?
( i assume its analytic ?? for complex z_i : z1 {z2} z3 ? )
furthermore , i have no idea why JmsNxn thinks x {1.5} 2 = x {0.5} x
???
tommy1729
