1.- You failed to present any precedents on the new simple methods based on the Rational Mean http://mipagina.cantv.net/arithmetic/rmdef.htm Which is the very essence of my first posting, so they were forced to try to rise many other issues and false statments to hide their incapacity and rash comments on this matter.
2.- You failed to present any posting from mine stating: "My methods always yield ALL THE BEST APPROXIMATIONS". They were challenged to do that but failed.
4.- You failed to try to discredit the new extremely simple high- order arithmetical algorithms by stating that they do not produce best approximations (which is of course another lie that anyone can confirm by reading my wepages). The litle envious man are not acquainted with the fact that any root- solving algorithm only need to hold true convergence towards the root-value (according to the standard convergence criteria), so the issue on best approximations is by no means a requisite for being considered as a trully good algorithm. Their ignorance on mathematics does not matter, at all, but their psychopathic behavior and stupidity is really disgusting.
3.- You showed a shameful unethical and psychopathic behavior and huge cheeks, and of course a cowardly tendency to anonymity. So this litle envious man cannot put his signature to his rash comments.
4.- You failed their attempts to try to divert the issue on root- solving to the issue on philology and gramatical use of the phrase : "GENERALIZED CONTINUED FRACTION". And you were not acquainted with the fact that one of the most important characteristics of the very particular sample on GCF shown in the webpage: http://mipagina.cantv.net/arithmetic/gencontfrac.htm IS THAT SUCH GCF IS JUST A REPRESENTATION OF DANIEL BERNOULLI'S METHOD FOR ROOT-SOLVING, which at the same time is es PERIODIC CONTINUED- FRACTION REPRESENTATION of irrational numbers of degree higher than 2. With the particularity that all this concept was TRIVIALLY devised by agency of the Rational Mean processes. Your stupidity, envy, cowardice and psychopathic behavior drived you to fall in such a rat-trap which has been specially settled for overbearing ignorants like you. So anything you want to tell about such GCF is automatically applied to Daniel Bernoulli's method. Now, you want me to explain to you how the Lineal Homogeneous Recurrence Relations of Daniel Bernoulli's method works with complex numbers. WRONG, take a book by yourself and learn that method, and slow down your overbearing ignorance.
Based on the above considerations, I face and maintain what follows and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
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