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between addition and multiplication
#18
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
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Messages In This Thread
between addition and multiplication - by lloyd - 03/10/2011, 09:10 PM
RE: between addition and multiplication - by tommy1729 - 03/15/2011, 10:22 PM

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