On 26 jul, 05:33, "sttscitr...@tesco.net" <sttscitr...@tesco.net> wrote: [cut ]
Unidentified person, it is so easy for you to insult because you are hiding your name. Indeed, I have never intended to be rude but you have shown a psychopathic behavior. The requisite for any root-solving algorithm to be considered as that, is NOT about if it yields best approximations, is about its true convergence to the root, there is plenty info on convergence criteria. If the algorithms yield best approximations then that's great?, that's fine, but best approximations are not the requisite for asserting that a method converge. indeed, you are certainly showing a psychopathic behavior in the same way as others did in the past (I am not quite sure if you are one of them hiding your name).
Of course, the methods shown in my webpages embrace --among many other new algorithms-- the traditional continued fractions of second degree, Newton's method, halley's method, Householder's method etc. and certainly yield best approximations. That's true and anyone can see that in my webpages.
I even understand your feelings, probably you have read some books on numerical methods (based on infinitesimals, fluxions, etc.) and the history of root-solving, and now you realize that halley's, Householder's methods for approximating roots as well as many other new iterating functions could have been TRIVIALLY developed by means of the MOST SIMPLE ARITHMETIC.
That is bitter blow for you and some others. I am sorry for you but you have to swallow it.
But... *************************************************************************** I have never asserted in any posting from mine nor in my webpages, nor in my book, nor in any paper that:
"The methods shown in my webpages yield ALL THE BEST APPROXIMATIONS".
There is nothing by far similar to such assertion in my webpages and postings. That's why I posted again my first posting in this and other threads. Of couse, these new simple arithmetical methods yield best approximations and have high-order convergence speed, and noone can deny such a STRIKING FACT.
You just need to show to the sci.math audience just a single phrase from mine stating: "The methods shown in my webpages yield ALL THE BEST APPROXIMATIONS".
But you cannot because that is another lie from yours pretending to cause confusion as some others tried in the past and had no success.
there is nothing there by far similar to that you are trying to falsely state, that is: "The methods shown in my webpages yield ALL THE BEST APPROXIMATIONS".
The sci.math audience can see that you have no choice but to insult, you and your friend have shown an unethical attitude and you should cogitate on that. I have nothing more to add about the unethical attitude from you and your friend. Ask to Newton's , Halley's, etc. whatever you want to ask I have no intentions to answer any other question from you and your friend Grover Hughes.
If you think that you can make me upset, your are WRONG, so WRONG. I do not look for any favors from neither any intitution nor any peer- review journal. I really enjoy what I am doing: TO TELL THE CRUDE TRUTH ABOUT THE WHOLE HISTORY OF ROOT SOLVING.
I only regret that your so low self-esteem leads you to set such a shameful example to young students. I regret that so much.
The simple high-order methods shown in my webpages have demolished others in the past in the same way as they have done with both of you (might be that some of you could be some of them, whatever...I do not care). I even understand your feelings, probably you have read some books on numerical methods and now realize that halley's, Householder's and many other new iterating functions could have been developed by means of the MOST SIMPLE ARITHMETIC.
That is bitter blow for you and some others, I am sorry for that but you have to swallow it.
>From now on you will get the same message I gave to both of you last time:
On 24 jul, 17:07, gwh <ghug...@cei.net> wrote:
> On Jul 24, 9:36 am, arithmonic <djes...@gmail.com> wrote: > My, my! Leave town for a few days, and look what happened while my > back was turned! I've never been so popular before, and all because I > remarked that an old text showed how to extract cube roots! Well, here > it is-- I'll do the best I can to type it in a form that I hope will > be readable.
YOU mr. Grover Hughes GOT A CHEEK, INDEED. YOUR UNETHICAL ATTITUDE ONLY MATCH THAT FROM OTHERS IN THE PAST IN THIS NEWSGROUP. EXACTLY THE SAME UNETHICAL ATTITUDE.
WHAT FOLLOWS IS WHAT THIS GUY Grover Hughes RESPONDED TO MY ORIGINAL MESSAGE:
Grover Hughes negligently and unethically 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.
FOLLOWS WHAT HIS UNIDENTIFIED FRIEND <sttscitr...@tesco.net>
UNETHICALY AND 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
Both assertions from Grover Hughes and his unidentified friend <sttscitr...@tesco.net> has been proven to be absolutely FALSE and UNETHICAL STATEMENTS. Their alleged Hurtwitz 's method (which in fact his originator was Achimedes or Wallis if you prefer) and Eshbach's method are not, by any means, the same to 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 maintain 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 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 things could have been missed. 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.
All those ranting raving messages, unethical actions, and insults against me have no importance, at all.
What really matters is that : "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.
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.