On 7 ago, 18:06, mike3 <mike4...@yahoo.com> wrote: > On Aug 6, 8:18 am, arithmonic <djes...@gmail.com> wrote: > > > Come on, continue by insulting the author of such book (and other > > related people), I am sure that they do not agree with most of my > > critics to the root-solving history and I do not want them to do so, > > but they are true un-biased mathematicians. > > > Come on, persistent offender. > > > Show some precedents on the methods shown in my webpages. > > Ignore the guy's childish insults, drop your > OWN childish insults and RESPOND TO HIS POINT: > > "Generalized continued fractions should exhibit > the same properties as simple continued fractions. > SCFs produce best rational approximations, > generalized continued fractions should produce best > simultaneous approximations. > If the rational mean can produce generalized > continued fractions, it should produce all > best simultaneous rational approximations. > If it can do this it can then solve the cubic Pell, > whose solutions are best rational simultaneous > approximations to cubrt(k*k), cubrt(k). " > > Can you do that, with LOGIC?
What make you think that you are the one who can impose what the scope of the phrase "GCF" is? or what such phrase means? You and the other guy did not put your signatures on your postings while the author of the following book certainly did. What make you think that your comments are worth of any consideration?
The very particular "Generalized Continued Fractions" developed by agency of the Rational Mean and shown in my webpages do not bring a solution for the general pell's equation, and neither I nor my webpages, nor any posting from mine states that they do such thing. They only bring a Generalization of Periodical Representation or high- order irrational numbers, that is clearly stated in my webpages, even with numerical samples.
Standard Continued Fractions have so many properties, if you can find any high-order generalization for any of their properties then you are free to use the phrase GENERALIZED CONTINUED FRACTION , because you have found a very particular generalization os stantard continued fractions, that's it. in my case the property is: Periodic representation of irrational numbers of higher degree.
ing. Domingo Gomez Morin Structural Engineer Caracas Venezuela