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

 Messages: [ Previous | Next ]
 arithmetic Posts: 106 From: venezuela Registered: 1/23/06
Re: cube root of a given number
Posted: Aug 12, 2007 2:31 PM

SUMMARY:

At the thread entitled: "cube root of a given number":

I said:
On 14 jul, 23:30, arithmeticae <djesusg@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.
> Don't forget to take a look at the links and references:http://mipagina.cantv.net/arithmetic

and some people replied by saying the the methods shown in my webpages
and book could be of some interest to people.

sttscitrans@tesco.net replied by saying:

On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
> On 16 Jul, 06:13, Gottfried Helms <he...@uni-kassel.de> wrote:
> I don't think the claim that these methods are in any way
> new stands up to scrutiny.
> The idea of Farey dissections is clearly not new.
> It is mentioned in Hardy and Wright for example.
> Hurwitz wrote a paper "Ueber die Irrationalzahlen"
> in the 1890s which describes a "mediant" method based on Farey
> fractions that produces best rational approximations.

first of all, notice that my work is about root-solving algorithms,
not about best-approx. algorithms, there is a
huge difference between them. I have never talked about "best-approx.
algorithms", neither in my webpages,
nor in my book, nor in any posting form mine:

http://mipagina.cantv.net/arithmetic/rmdef.htm

Notice that at this point "sttscitrans" was trying to state that my
root-solving methods were not new, at all, because Farey Fractions
have been used since long time ago. Also, he introduced the phrase
"best approximations" because in his next postings
he will try to state that Hurtwitz's method is better because it
yields ALL the best approximations while my methods
do not always do that.
Only a crank like this sttscitrans@tesco.net (who someday came to
realize that imaginary numbers
actually cohabit with virusses. For God sake?) could ever bring to
light an insane argument like that.
Following his cranky line of thought then no methods in this planet
earth is in any way new
because almost all known numerical methods use Additions and such
since ancient times.

Worst, another thing that he is trying to state and can be easily
understood from his overbearing cranky words
is that Hurtwitz and others made all (Everything) that could have
ever been done on root-solving algorithms and Best approximations,
so any claims on any "new root-solving methods or best-approx. methods
are non-existent for him,
simply, they do not stand up for scrutiny.
In other words, in his imperiousness he thinks that Hurtwitz worked
ALL the existent Mediant combinations that you can operate
with any set of rational numbers, so there is no chance for new
combination to be done.
At this point it must be said:
1.-The Mediant only works with reduced fractions and only yield
reduced fractions
2.- The General Rational Mean concept works with both reduced and non-
reduced fractions and
can yield any of them, I mean, when you operate the Rational Mean
exclusively with Non-reduced fractions then you
can obtain either reduced or non-reduced fractions. So in order to try
to find a method for yielding all the
best approximations you are not obligued to restrict yourself to use
exclusively the Mediant and Farey Fractions as Hurtwitz and many
others always did.
I insist that I am only intending to show that Hurtwitz and others did
not make all that can be done about best approximations
because there are certainly many other ways to try this by agency of
the Rational Mean and
that is one of the uncountable things that the new methods shown in my
webpages are pointing out.
I repeat, the rational methods shown in my webpages do not yield all
the best approx., I have never said that, but they are
pointing out new ways that surprisingly neither hurtwitz nor any
others (from Babylonian times up to now) tried in their works, mainly
because they all restricted themselves to the analysis and use of just
Reduced Fractions and the Mediant.
Notwithstanding, the methods shown in my webpages are not about best
and generalized periodical representions of irrational numbers. That's
it.

In his subsequent ranting-raving postings sttscitrans also stated that
my methods do not stand up to scrutiny because
they do not always yield ALL best approximations.
Again, following the cranky sttscitrans's line of thought anyone could
argue that Newton's, Bernoulli's, Halley's methods
do not stand up to scrutiny because they do not yield ALL the best
approximations all the time,
as his alleged Hurtwitz's method do.

What a crank, indeed. It is so hard for a rational person to begin any
discussion on any issue by departing from
such cranky arguments, so one has to deal with the following options:
1.- The guy is an ignorant or is just making some fun
2.- The guy is either a real crank or just a biased-spiteful
mathematician who got hurt so bad because of my postings, mainly
because
he cannot show any precedent on the extremely simple high-order
algorithms shown in my webpages. So, he decided
to attack by any means and to cause some confusion on the issue.

I know very well the price one has to pay for telling some truths
however, I am happy for being free to do so. By this very moment I
certainly know there are
many un-biased and wise mathematicians in many countries that think
they do not own the Truth,
and are even willing to admit that it is a bit odd that this extremely
simple methods do
not appear in the math literature, and consequently there is so much
the way root-solving methods were conceived all through the history of
maths.

Of course, sttscitrans's cranky arguments were not going to help him
so his cranky messages got worse when a guy called Grover hughes
replied to my first posting:

On 17 jul, 04:38, "sttscitrans@tesco.net" <sttscitrans@tesco.net>
wrote:

> On 16 Jul, 23:24, gwh <ghug...@cei.net> Grover Hughes 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. I
> > used that method lots of times in my engineering career when I needed
> > more precision than my trusty log-log duplex decitrig slide rule was
> > able to give me.
> > Grover Hughes

>
> Yes, you can find interesting
> pre-computer techniques in
> old maths books - even the" texts on
> numbers". Was there a reference to
> to the originator of the method ?

Notice how "sttscitrans" firmly endorsed Grover Hughes' assertions.
So, I challenged them to show such Eshbach's method but Grover Hughes
abandoned the
discussion for many days, so the guy called "sttscitrans" in his
desperation
and anguish cried out:

> > On 24 jul, 06:44, "sttscitrans@tesco.net " <sttscitrans@tesco.net wrote:
> > > [cut], ... It would be interesting if he [Grover Hughes] could post the method
> > > he found in the Handbook...

I continued by challenging both of them, and "sttscitrans" felt
himself
forced to say "I'm sure the poster [Grover Hughes] knows what he

On 22 jul, 07:29, "sttscitrans@tesco.net" <sttscitrans@tesco.net>
wrote:
> > On 22 Jul, 04:28, arithmonic <djes...@gmail.com> wrote:
> > 1.- I challenge you to show such Eshbach's method in this thread,
> > because both of you are trying to state that my methods --based on the
> > Rational Mean-- are the same as the one you read in Eshbach's
> > work ("Handbook of Engineering Fundamentals).

>
> I'm sure the poster [Grover Hughes] knows what he read.

Notice how "sttscitrans" again endorses Grover Hughes' assertions,
that is, it is about the third time he have
assured that the methods shown in my webpagea are not new and they can
be found in the literature.

After so many days, Grover Hughes finally brought to light a TRIAL-&-
ERROR method that had no connection,
at all, with the extremely natural and simple high-order arithmetical
root-solving methods shown in my webpages.
This is what Grover Hughes showed up:
On 24 jul, 17:07, gwh <ghug...@cei.net> 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 [...CUT, the unrelated numerical sample he brought to light]

Notice that in his previous posting Grover Hughes asserted: "...the
cube root extraction scheme described
there [Eshbach's handbook] was precisely the same as the scheme
described on [my web pages. CUT...]"
Grover Hughes finally gave up and run away, of course, by previously
shouting some attacks ad-hominen against me.

At the same time "sttscitrans" in response to my challenge showed up
his Hurtwitz'method which yield
all the best approximations, and alleged that my methods do not stand
up for scrutiny because Hurtwits's
method was basically the same than those shown in my webpages.
Of course, that's not true. That's a sttscitrans's lie.
Hurtwitz might well have worked with Mediants the way he liked, but
such alleged Hurtwitz's method
is actually the ancient Archimedes's Mediation which was used by other
mathematicians as Wallis, Chuquet, etc.
All that is is fully explained in my webpages and book. Such alleged
Hurtwitz's method is the slowest method
you could ever find, worst, it is an ancient TRIAL-&-ERROR nightmare
because you need to check
--at each step of the process-- that your approximation is by defect
or excess,
and that is a cranky task: One has to raise each approximation to the
n-th power in
order to check if it is lower or higher that the n-th root. What a
silly deal, indeed.

So I also explained to 'sttscitrans' that he didn't showed up an
algorithm but just an ancient TRIAL-&-ERROR nightmare,
a cranky task, which cannot be compared --by any means-- to the
Natural Arithmetical High-Order root-solving Methods shown in
my webpages (New arithmetical methods that do not use any trial-&-
error checkings).
The methods shown in my webpages are truly Natural in the sense that
they do not require any TRIAL-&-ERROR checkings.

By this very moment, 'sttscitrans' realized that al his attepts
failed.
So his desperation became transfigured into anger and hate, and he
started to attack ad-hominen as well
as to try to divert the main issue of the thread.

Now, this crank 'sttscitrans' had nothing but to argue that because I
used the name "Generalized Continued Fractions"
for naming a very particular generalization of periodic representation
of irrational numbers of higher degree
shown in another wepage from mine (which by the way I did not mention
in my posting to this thread)
then it is clear for him that I am claiming that my methods solve the
general pell's equation and
called me liar and insulted me by many ways.
Notice that at this point 'sttscitrans' had nothing else to discuss
but just about the use of a phrase.

I clarified the point by explaining that the expression shown at:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
is certainly a generalization of a very particular property of
standard continued fractions and that there are wise mathematicians
who have used the name in exactly
the same way:
As evidenced in pages 3-4, 1.1.1., "Generalized continued Fractions":

http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf

At this point, this crank even dare to raise the name of my country,
in the same way others already did in the past.

The true fact is that some guys really hate to see a SouthAmerican man
the "holy" Root-Solving History. They just want third-world people to
praise their high ideas
on Trial-&-error geometrical methods, to praise their so-elevated
Tricks-&-Patches Science, to contemplate
their construction of a science devoted to raise funds and yield
inmediate results at any cost.

Showing his high imperiousness and deep contempt for anything that a
Southamerican guy could have ever discovered,
this crank 'sttscitrans' when reffering to the methods shown in my
webpage, said:

*************************************************
*************************************************
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
when referring to my stuff wrote:

>...who but a retard would wriite it down for posterity ?
*************************************************
*************************************************

his cranky behavior drived him to include in his shameful insults
other people who have certainly
written something about the new methods shown in my webpages.

He not only insulted the author of the aforementioned webpage:

http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf

but many others that he can meet at:
http://mipagina.cantv.net/arithmetic

But, that's not all.

When he finally realized that all his attempts were just crushed by
the new general Rational Mean concept,
he decided to divert, again, the main point of this discussion to the
issue on Imaginary Numbers. Now by stating that imaginary numbers are
alive in the same way as virusses are.

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