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":
http://groups.google.com/group/sci.math/browse_frm/thread/1980f24c967116a3/42982f76fef5e82e?utoken=z0nC2ysAAADVrFBENlY72krdcnErBvJDSVGlHgnf9ZOdCcWhWQvC5u3SqHm3vJ51FaKJlBbL0
I said: On 14 jul, 23:30, arithmeticae <djesusg@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. > 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...@unikassel.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 rootsolving algorithms, not about bestapprox. algorithms, there is a huge difference between them. I have never talked about "bestapprox. 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 rootsolving 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 operation was already invented 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 rootsolving algorithms and Best approximations, so any claims on any "new rootsolving methods or bestapprox. methods are nonexistent 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 Nonreduced fractions then you can obtain either reduced or nonreduced 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 approximations but about rootsolving algorithms and generalized periodical representions of irrational numbers. That's it.
In his subsequent rantingraving 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 biasedspiteful mathematician who got hurt so bad because of my postings, mainly because he cannot show any precedent on the extremely simple highorder 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 about the history of rootsolving, however, I am happy for being free to do so. By this very moment I certainly know there are many unbiased 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 to inquire about the the way rootsolving methods were conceived all through the history of maths.
Of course, sttscitrans's cranky arguments were not going to help him in his causingconfusion task 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 loglog duplex decitrig slide rule was > > able to give me. > > Grover Hughes > > Yes, you can find interesting > precomputer 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 read":
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 highorder arithmetical rootsolving 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 adhominen 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 nth power in order to check if it is lower or higher that the nth 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 HighOrder rootsolving 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 adhominen 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 34, 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 making such sound critics about the "holy" RootSolving History. They just want thirdworld people to praise their high ideas on Trial&error geometrical methods, to praise their soelevated 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.

