arithmetic
Posts:
106
From:
venezuela
Registered:
1/23/06


Re: cube root of a given number
Posted:
Jul 27, 2007 12:17 AM


On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net> wrote: > 1. Failed to present any precedents on the new simple > methods based on the Rational > Your method is facile, who but a retard would wriite it down > for posterity ?
I was sure that you was close to begin to cowardly insult many other people (who are not inhabiting this newgroup) as everybody can meet at the links included in the webpage : http://mipagina.cantv.net/arithmetic
Generalized Continued Fractions is another issue, and is clearly explained at the webpage: http://mipagina.cantv.net/arithmetic/gencontfrac.htm
The issue on the way continued fractions have been treated all through the history is precisely the essence of critics of that GCF webpage. The most relevant aspect of these very particular Generalized Continued Fractions is that they allow to find periodic representations of irrational numbers of higher degree. And such GCF were devised exclusively by agency of the Rational Mean, that's what all my postings and webpage state.
Neither one single posting from mine, nor the GCF webpage state that such generalization of continued fractions yield all the best approximations for all the irrational numbers. On the contrary, the webpage only talks about a new periodic representation of irrational numbers of degree higher than 2, and bring numerical samples which clearly show that, for instance, in the case of the cube root some convergents are best approximations while others not. And your psychopathic and coward behavior cannot hide such numerical samples.
So you want me to name those fractions the way you want? You are wrong, a real imbecile like you that feel yourself so brave by hiding your name behind a computer and insulting people, cannot bring anything of interest to me. Cowards have nothing to bring, indeed. Why do you hide your name? What are you afraid of? Neither you, nor any other person HAVE INVENTED any single "Generalized Continued Fraction" bringing ALL THE BEST APPROXIMATIONS as well as the periodic representation of irrational numbers of degree higher than 2.
So, the only thing that make you think that you can make your stupid comments and insult people the way you do, as well as to force others to name something (that you are absolutely unable to invent) the way you think it should be, is only your psychopathic behavior.
The word "Continued" does not mean anything related to best approximations, that's why mathematicians had to create the phrase "Simple Continued Fractions" so it can be differentiated from those who not necesarily yield all the best approximations. Of course, that's so hard to understand for you. You even pretend to ignore that such words (even the word: "Simple") has been an issue for debate among many people.
You are a complete parrotfashion psychopathic coward who does not have the slighest idea of the implications of what you write. You only use to repeat all what you have read parrotfashion. That is the way you think about mathematics: Parrotfashion talking, like a zombie. A truly parrotfashion liar who now pretend to divert all the original discussion from rootsolving algorithms to philology and gramatical issues about GCF. JUST BECAUSE ALL YOUR LIES AND THOSE FROM Grover Hughes FAILED THEIR PURPOSE OF TRYING TO CAUSE CONFUSION ON THE LACK OF PRECEDENTS OF MY METHODS. You are just a coward.
You do not know a single bit about mathematics, you only use to repeat all what you hear from others' papers and then repeat all that showing a parrotfashion psychopathic behavior.
It is so easy to insult hiding yourself behind your computer. I wonder how it feels being such a coward, indeed. My name is DOMINGO GOMEZ MORIN AND I LIVE IN CARACAS, VENEZUELA. You are just a coward.
Traditional use of the phrases "Simple continued fractions" and "Continued fractions": 1. SIMPLE CONTINUED FRACTIONS: Always yielding reduced fractions. 2. CONTINUED FRACTIONS: Do not necessarily yield reduced fractions, but sometimes they do.
THE WORD "SIMPLE" HAVE BEEN ALWAYS USED TO DIFFERENTIATE THEM (1 and 2). So the word "SIMPLE" plays a very important role.
If one could have some "generalized expression" exhibiting the exclusive generation of reduced fractions like the aforementioned "SIMPLE CONTINUED FRACTIONS"(1), then you should call them: "GENERALIZED SIMPLE CONTINUED FRACTIONS" . The word "simple" have been always related to the generation of REDUCED FRACTIONS so you must use it somehow when constructing a generalized expression for it.
If you just want "GENERALIZED CONTINUED FRACTIONS" which do not necessarily yield best approximations but exhibit other very important properties as for instance the periodic behavior of irrationals of higher degree than 2 (as shown in my webpages) then you can call them: "GENERALIZED CONTINUED FRACTIONS".
Summarizing the reasons for the name "GENERALIZED CONTINUED FRACTIONS":
a. They are "GENERALIZED" because they are certainly a GENERALIZATION of traditional CONTINUED FRACTIONS (2), if they were a generalization of traditional "SIMPLE CONTINUED FRACTIONS" then you should call them "GENERALIZED SIMPLE CONTINUED FRACTIONS" or "GENERALIZED REDUCED CONTINUED FRACTIONS" or any other name making any reference to the exclusive generation of reduced fractions.
b.They are CONTINUED just because they are CONTINUED.
c. They are fractions just because they are FRACTIONS.
It is a typical psychopathic parrotfashion behavior to try to impose to others whatever you want but really can't do such thing. Sorry but you can't. I know that some others have negligently used the name "GENERALIZED CONTINUED FRACTIONS" in exactly the same wrong way as you pretend to do, but YOU ARE WRONG. You are just repeating just what you have seen that others did, you are just an anonymous psychopath who does not have the slighest idea of the implications of what you write, you only use to repeat all what you have read parrotfashion.
A truly parrotfashion liar who now pretend to divert all the original discussion from rootsolving algorithms to philology and gramatical issues.
so...eat this:
On 24 jul, 17:07, gwh <ghug...@cei.net> wrote:
> On Jul 24, 9:36 am, arithmonic <djes...@gmail.com> wrote: > BTW, does arithmonic always get so excited and upset? I never intended > to help his ulcer along...... > Regards, > Grover Hughes retired engineer, Sandia National Laboratories Ocultar texto de la cita 
Be sure Mr. unethical Grover Hughes that I will never get any ulcer from people like you and your friend.
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.
On 24 jul, 17:07, Grover Hughes gwh <ghug...@cei.net> unethicaly 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:
When I said:
> On Jul 14, 10:30 pm, arithmeticae <djes...@gmail.com> wrote: > > If you really like to analyze the most simple highorder rootsolving 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.
Grover Hughes negligently and unethically wrote: On 16 jul, 18:24, gwh
<ghug...@cei.net> wrote: > 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.
ALSO 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 HIGHORDER 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 mathhistorian 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, Platón, Nichomacus, Wallis, etc. would had found such highorder arithmetical methods in such a trivialarithmetical 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 mathteachers 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 HIGHORDER 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 mathhistorian will be able to deny such a crude fact.
I even understand your feelings, probably you have read some books on numerical methods and the history of rootsolving, and now you realize that halley's, Householder's and many other new iterating functions could have been developed by means of the MOST SIMPLE ARITHMETIC since ancient times, but mathematician of past times didn't develope such trivial highorder methods.
That is bitter blow for you and some others, I am sorry for that but you have to swallow it.
Ing. Domingo Gomez Morin Caracas venezuela

