Now, I am free to respond to BOTH OF you as you deserve before the sci.math audience because it has been proven that you and your friend Grover Hughes were making just FALSE STATEMENTS.
Grover Hughes negligently wrote: On 16 jul, 18:24, gwh <ghug...@cei.net> wrote: > On Jul 14, 10:30 pm, arithmeticae <djes...@gmail.com> wrote: > > If you really like to analyze the most simple high-order root-solving algorithms then you should take a look at: > >http://mipagina.cantv.net/arithmetic/rmdef.htm > > It is striking to realize that these new extremely simple artihmetical algorithms do not appear in any text on numbers since Babylonian times up to now. > > Maybe not in "any text on numbers", but back in 1945 I purchased a > copy of "Handbook of Engineering Fundamentals", by Eshbach, and the > cube root extraction scheme described there was precisely the same as > the scheme described on one of the links given on the above website.
and his friend also <sttscitr...@tesco.net> negligently wrote:
On 24 jul, 06:44, "sttscitr...@tesco.net" <sttscitr...@tesco.net> wrote: > Your historical claim may well be true, but at > least one poster states he has a reference predating your > claim. It would be interesting if he could post the method > he found in the Handbook
All the two assertions from Grover Hughes and his friend <sttscitr...@tesco.net> has been proven to be absolutely FALSE and UNETHICAL STATEMENTS. Their allegued Hurtwitz 's method (which in fact his originator was Achimedes or Wallis if you prefer) and Eshbach's method are not by far the same that the ones shown in my pages.
Notwithstanding, forget it, I do not care of such unethical attitude as well as i did not care for the shameful attitude from others in the past, the main point that I really care is the following:
I face and mantain my assertions: "THE EXTREMELY SIMPLE HIGH-ORDER METHODS SHOWN IN MY WEBPAGES --BASED ON THE RATIONAL MEAN-- 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. And this is a real shame mainly for all of us who have read some about the very long history of root solving.
What do think it would had happened if, for instance, Plat?n, Nichomacus, Wallis, etc. would had found such high-order arithmetical methods in such a trivial-arithmetical way? Consider that all those mathematicians from past times (including Newton, Halley, etc.) certainly had the elementary tools to do that, however, from the evidence at hand THEY DIDN'T, and this is something really striking for anyone who have ever read a book on the history of mathematics.
If these methods --based on the RATIONAL MEAN-- would had been discovered in past times then it is for sure that your math-teachers would had taught them to you at school. that's simple.
That is what really matters here, because this leads to think how many other thing are we missing. I am sure there another very different mathematics from that we have inherited and all these new simple methods are a clear evidence of that. There is certainly a missing mathematics and young minds certainly have the most simple tools to find it. we have to break the chains from past times.
On 24 jul, 12:41, "sttscitr...@tesco.net" <sttscitr...@tesco.net> wrote: > On 24 Jul, 16:12, arithmonic <djes...@gmail.com> wrote: > > > ************* > > But your statement about that I claimed to have solved the cube Pell's > > equation is another absolute FALSE STATEMENT from yours. > > No, you have obvuiosly forgotten, my comments on > your insane rantings some years ago. > > You should be able to find them by searching for > Morin, Davidson, Pell. > > You were also claiming that your methods could solve > the standard Pell equation. Claims which also > turned out to be wrong. You have never > admiited that you were wrong. But that would be too much > to expect.
Yes, in this newsgroup you and some others guys in the past tried to do exactly the same unethical acts than you and your friend Grover Hughes have tried this time. You got a cheek, indeed. You and all your friends should cogitate on your unethical attitude.
In past times, You insisted to say that the methods shown in my webpages do not yield best approximations and I told you and again I tell you this time that such methods certainly produce best approximations. The fact that some of those methods based on the Rational Mean could not produce ALL the best approximations is another problem which is the same problem with Newton's, Halley's, etc. when computing some particular roots.
I challenge you to show a posting from mine saying exactly what you are attributing to me, that is: "I can solve the cube version of Pell equation" That is another FALSE STATEMENT FROM YOURS, as FALSE as all the other statements that you and your friend Grover Hughes pretended to state in order to prevent people from reading my book and webpages. But you have failed again in the same way that in past times you and others did.
You, your friend Grover Hughes and some others from past times have had the same unethical attitude, many of you use to form kind of packs and make all kind of FALSE statements causing confusion and preventing people from reading one's work. That's an unethical attitude.
But, you know? I don't care and I have never cared of such packs and unethical attitude, because the methods shown in my webpages easily demolish all such unethical attempts, and such trivial high-order methods will remain there even after I have died out.
What I have always said is that my methods embrace Newton's, Bernoulli's, Halley's, Househloder's and many other NEW iterating functions for solving roots. My method is not just one algorithm but a new general and very simple concept involving so many high-order methods. The point these methods are based on the most simple arithmetic and that is really striking mainly when considering the very long story on root-solving.
The methods shown in my pages : http://mipagina.cantv.net/arithmetic/rmdef.htm DO CERTAINLY YIELD BEST APPROXIMATIONS, of course they CERTAINLY DO, and I AM SURE that the NEW ARITHMONIC MEAN is the best tool to work the cube version of PELL'S EQUATION, and that is all what I have ever said. IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC MEAN PROCESSES SHOWN IN MY WEBPAGES. That hurt yours and some others feelings (mainly math-historians) but that's not my fault, ask mathematicians from past times why they didn't developed such TRIVIAL HIGH-ORDER ARITHMETICAL NON-TRIAL-&-NON-ERROR ALGORITHMS.
I have no intentions of sending these NEW methods to any peer-review journal, I don't need to give detailed explanations on why, I think my reasons are very fairly clear. I think this is matter of ETHICS, MORAL AND UN-BIASING MATHEMATICS.
If a math-historian take a look through all those new simple arithmetical methods --based on the rational mean-- the such mathematician must have the MORAL OBLIGATION to make comments and include some analysis on them in his books, papers, etc. THAT JUST A MATTER OF MORAL AND ETHICS, MAINLY WHEN CONSIDERING THE VERY LONG STORY ON ROOT-SOLVING.