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Topic: cube root of a given number
Replies: 112   Last Post: Jan 10, 2013 1:39 PM

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arithmetic

Posts: 106
From: venezuela
Registered: 1/23/06
Re: cube root of a given number
Posted: Jul 26, 2007 7:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 26 jul, 12:24, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
> On 26 Jul, 14:29, arithmonic <djes...@gmail.com> wrote:
>

> > On 26 jul, 04:37, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> > wrote:
> > [cut sick and cowardly behavior hiding his name]

>
> Generalized continued fractions should exhibit
> the same properties as simple continued fractions.
> SCFs produce best rational approximations,
> generalized continued fractions should produce best
> simultaneous approximations.
> If the rational mean can produce generalized
> continued fractions, it should produce all
> best simultaneous rational approximations.
> If it can do this it can then solve the cubic Pell,
> whose solutions are best rational simultaneous
> approximations to cubrt(k*k), cubrt(k).
>
> You are a complete idiot who does not have the
> slighest idea of the implications of what you write.




You are a complete 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 parrot-fashion. That is the way you
think about mathematics: Parrot-fashion talking, like a zombie.
A truly parrot-fashion liar who now pretend to divert all the original
discussion from root-solving algorithms to philology and gramatical
issuesABOUT 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 parrot-fashion 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 parrot-fashion 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 parrot-fashion.

A truly parrot-fashion liar who now pretend to divert all the original
discussion from root-solving 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 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.



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 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, Platón,
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.


I even understand your feelings, probably you have read some books on
numerical methods and the history of root-solving, 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 high-order 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



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