Wondering about Domingo's Rational Mean book

[Kirby Urner]

"Iain Davidson" <Sttscitrans at tesco.net> wrote:

>
>Kirby Urner <urner at alumni.princeton.edu> wrote in message
>news:c588jscm3oqjlfnc723pmafemjcl99ihpm at 4ax.com...
>>
>>
>>
>>
>> Have folks on sci.math already discussed
>> http://www.etheron.net/usuarios/dgomez/Roots.htm
>> to anyone's recollection?  I'd be interested in
>> comments and/or pointers to previous postings.
>
>The advantage of standard CFs is that they produce all
>best approximations. The mean method for cbrt(2)-1 misses
>131/ 504, for example.
>

I presume by "best" you mean most accuracy for the least
digits.  Like, the mean method gets me closer to cbrt(2)-1 
than 131/504 with fractions like 4159/16001 or 236845/911219 
or 168286661033/647452990441 -- but you're saying standard
CFs will converge more quickly, yes?  

In other words the standard CFs will give a better approximation 
when pushed to the same total number of digits -- something 
along those lines?

Forgive my ignorance, but this is not my field of expertise.

Do you know of an URL where the standard algorithms for 
approximating the nth root of k as p/q are spelled out, 
something suitable for computerizing?  

I'd like to code an algorithm that _does_ hit 131/504, and 
compare it with the mean method for other values -- just 
for kicks (plus I'm seeing applications in early math ed,
when ideas about fractions and roots are first being defined).

Kirby