He also use the name "Generalized Continued Fractions" for my periodical high-order expressions. He asserts that can be various types of "Generalized Continued Fractions" according to the very specific CF property that has been generalized.
Why you didn't continue by insulting him this time? Why you didn't continue by calling him retard this time?
You certainly said: >...who but a retard would wriite it down for posterity ?
Why are you so coward?
Why you raised the name of my country in your last posting?
There are many reasons for all that:
1.- You are a coward that thinks that you can insult any Southamerican guy the way you want. You think that you can be a persistent offender and nothing will happen just because it is just a LatinAmerican guy. That's the main reason you are not willing to insult him (and many others from other countries) but prefer to insult the LatinAmerican guy and tell lies about his work.
2.- The other reason is that you really HATE, so much, to see this SouthAmerican guy telling you these truths about the whole history of roots solving, and teaching you these new extremely simple high-order methods, mainly, when considering that you are incapable of showing any single precedent on them since Babylonian times up to now. It is a real disgrace for you to be forced to swallow all this, mainly when considering that you have been crushed just by a Civil Engineer, not a mathematician. So, I understand how low is your selfsteem-level by this time, that's why you desperately need to insult and act as a persistent offender. Notice that you have been crushed by a humble SouthAmerican Civil Engineer in such a way that you had no other chance but to bring out a discussion on the way you demand that the phrase "Generalized Continued Fractions" should be used.
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 fairly clear stated in my webpages, and you certainly know that, but you just want to talk about your lies on that matter.
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.
You are clearly unable to realize that I don't care about the transcendence of such very particular GCF expression shown in my webpages, because there are many others generalizations that can be obtained by agency of the Rational Mean, and that is not the true issue of my work.
>"It is not clear which of the "two types" of generalized continued fraction Finch is referring to."
You have been finally crushed and forced to admit that there can be various types of generalized continued fraction. It seems that you think about yourself as a kind of "choosen" who will decide how to use mathematical phrases. You have been crushed and forced to slow your overbearing lies down.
That is what my posting demonstrate. Also it demonstrates that you do not want to talk about those extremely simple arithmetical "root- solving" methods (which is the very spine of ALL my postings), but just want to deviate the issue to "best approximations" and pell's equation and the use of the phrase "GCF".
-------------------------------------------------------- Just swallow what follows very gently, again and again, because this is what I have said all through my postings in many newsgroups, and that is precisely all what you want do not want to discuss by any means:
It is just disturbing to realize these so simple arithmetical methods DO NOT APPEAR in any book on numbers since ancient times up to now:
THESE SO SIMPLE METHODS DO NOT APPEAR IN NEITHER ANY CHINESE, NOR ARAB, NOR INDIAN, NOR WESTERN BOOK, since ancient Babylonian times UP TO NOW!!! AND YOU WILL REALIZE THAT NO MATHEMATICIAN nor any math-historian will be able to deny such a crude fact.
Whatever... There are very good news here, specially, for young people because from now on, by means of simple arithmetic they will be able to learn at secondary school --by means of the most simple arithmetic-- many new simple higher-order algorithms, as well as all those well-known cartesian-infinitesimal algorithms (i.e.: Halley's, Newton's, Bernoulli's and Householder's) which have been considered as superb achievements of the history of mathematics, however, one can see now that all those "superb" achievements can be easily developed by means of the most simple arithmetic.
Young student, be sure there is something very wrong with the whole Cartesian-Infinitesimal scheme we have inherited. Yours is the chance to find new ways on mathematics.
Ing. Domingo Gomez Morin Structural Engineer Caracas Venezuela