Wondering about Domingo's Rational Mean book"

[Iain Davidson]

<paraguana at my-deja.com> wrote in message news:8i7vo0$p8v$1 at nnrp1.deja.com...
> In article <8i5vsn$llr$71 at epos.tesco.net>,
>   "Iain Davidson" <Sttscitrans at tesco.net> wrote:
> >
> > > "Iain Davidson" <Sttscitrans at tesco.net> replied:

You haven't explained yet how your method finds best
approximations to sqrt(n) without first  knowing
a best approximation.
How would your method find all best approximations
to sqrt(61) ?


> Now, considering that this not a one-way discussion I´m sure you
> will be so kind and take some time to formulate here those CFs method
> you mentioned for finding a sequence of best approximations for the
> cube root of any number, I´m sure it will be amusing and very useful
> not only for me but for the whole audience of this newsgroup.

No I was not taking about best approximations to the cube root of a
number - you can do that with CFs.

What I was talking about was simultaneous approximation, say, of the
ratio cubrt(25): cubrt(5):1. As rational means are the basis of all
rational approximation theory,  you should be able to come up
with an effective method. After all, this is the claim you are
making.