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


Re: cube root of a given number
Posted:
Jul 24, 2007 10:36 AM


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
It is not just a problem on the false and unethical statements of your friend Grover Hughes who allegued that my methods were exactly the same than those from Eshbach's, 1945 "Handbook of Engineering Fundamentals". You endorsed his unethical claim and stated that he was right and my methods were not new, at all.
You and him are now facing nonethical, false and negligent statements before the sci.math audience.
Grover Hughes WILL NOT be able to prove his claim and you know that.
You also made other false statements trying to state that your alleged Hurtwitz's method (which is not Hurtwitz's but Wallis's) was the same than the ones shown in my webpages.
You accused me of being an ignorant on the rootsolving issue, while you even ignored that wallis was the originator of your alleged Hurtwitz'method, EVEN WORST, YOU ARE NOT ACQUAINTED WITH THE FACT THAT ACTUALLY WAS ARCHIMEDES THE TRUE ORIGINATOR OF SUCH PRIMITIVE AND SLOW TRIAL&ERROR METHOD, as you could have knew if you would had looked through my webpages. Notwithstanding, the problem is not about ignorance, that does not matter, the problem is about arrogance and contempt for my methods just because I say that "it is a shame that this methods do not appear in neither any CHINESE'S, nor EUROPEAN, nor ARAB, nor AMERICAN book on numbers since Babylonian times up to now. You and other should cogitate on ETHICS and UNBIASEDMATHEMATICS even considering that my claims hurt so much..
Anyway, I am glad to see that you are finnally realizing that these methods are BRAND NEW even considering that they are EXTREMELY SIMPLE and have HIGHORDER CONVERGENCE.
There is another thing I would be happy to see that you could also realize, that is, that the "Rational Processes" shown in my webpages ARE NOT just ONE method but an UNCOUNTABLE number of methods based on the RATIONAL MEAN embracing the wellknown Newton's, Bernoulli's, Halley's, Householder's methods as well as MANY OTHER new iterating rootsolving processes. The problem is that in order to realize that, you should have to take a look at my webpages and all we know that you WILL NEVER DEBASE YOURSELF by doing such thing. Just think about this, all those wellknown methods like Newton's, Householder's, Halley's, Bernoulli's and many other new ones, all of them trivially developed just by agency of the most simple arithmetic (THE RATIONAL MEAN),
Have you ever read a book on the History of mathematics?
What do think it would had happened if, for instance, Plat?n, Nichomacus, Wallis, etc. would had found such highorder arithmetical methods?
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. So, I would be so happy if you could also realize that.
> You make at least two mathematical claims about > your method that are false. (arithmetical operation, > best approximations).
There is another thing I would be happy to see that you could also realize, that is, that the "Rational Processes" shown in my webpages ARE NOT just ONE method but an UNCOUNTABLE number of methods based on the RATIONAL MEAN embracing the wellknown Newton's, Bernoulli's, Halley's, Householder's methods as well as MANY OTHER new iterating rootsolving processes.
So any complains from yours on the simple arithmetical methods shown in my webpages, are the same complains from yours on NEWTON'S, HALLEY'S, HOUSEHOLDER'S, BERNOULLI'S... methods.
So do not ask me about best approximations because it is clear that you should ask first those people.
Now in reference to the issue on "welldefined operation" I said that I will not discuss that in this thread, I have my theory about all that and is briefly explained in my webpages. I do not believe in the modern current stream of thought about rational and irrational numbers, of course it is related to Cartesian/deimal system, but that is another issue and you will not divert the original esence of this thread by introducing new issues in each posting.
******************************************************************************************************************** You and your friend Grover Hughes have not proved what you claimed about Hurtwitz and Eshbach, that's why I repeat to you:
NOTICE that your friend Grover Hughes have not shown any single proof of what he claimed, and left the discussion. what a cheek, indeed. That is totally unethical. You fully endorsed his unethical attitude and have not bring to light any evidence of what he claimed. Well, I think you have no problem with that because you do not give your name. On the contrary I do give my name and face all my assertions.
I can see you are also not willing to read any single bit of my webpages. All those references to the mediant you mentioned in this new posting from yours appear in my book and are briefly mentioned in my webpages, of course, it really proves that you are not willing to take a deep breath, count to ten and then take a look at my webpages.
I DO NOT USE the MEDIANT. The MEDIANT works only with reduced fractions, I work with the general concept that I have called "RATIONAL MEAN" because neither Cauchy, nor Charles de Comberousse assigned any name to such concept, probably because they do not considered the "RATIONAL MEAN" as a true operation in the set of rational numbers but just an operation of ordered pairs. So considering the differences between both concepts I had no choice and decided to use the name "RATIONAL MEAN".
According to modern mathematicians the MEDIANT is a "WELL DEFINED" operation within the set of rational numbers because it works with reduced fractions, while the "RATIONAL MEAN" (which does not work exclusively with reduced fractions) IS NOT WELL DEFINED within the set of rational numbers. That is the fundamental difference between both concepts, that is, according to modern mathematics they are two very different things even when they seems to be similar. Remember, the RATIONAL MEAN does not exclusively work with reduced frations. Of course, I have so much to say about those statments from modern mathematicians on their "well defined" concepts because I consider this is a crucial point and leads the way to a very different conception on mathematics, I mean, it could lead to a new true Natural Mathematical Science, however, I will not discuss that here, all this is explained in my webpage and my book: http://mipagina.cantv.net/arithmetic/rmdef.htm
You should be able to recognize the huge difference between "MEDIANTS" AND "RATIONAL MEANS" because you seems to like so much modern mathematics. I don't like the mathematics se have inherited, sorry for that.
I have never said that my using the Mediant or the Rational Mean is new. I have never said that, you are only generating confusion when stating that, on the contrary, my webpages and book contains full information on the precedents on the use of the Mediant. In my webpages I show that there have been some attempts to compute roots by agency of the MEDIANT, moreover, it is well known that the MEDIANT is the fundamental rule for the generation of convergents in the continued fractions of second order (as I use to call them)
What I have said is that the EXTREMELY SIMPLE HIGHORDER ROOTSOLVING METHODS shown in my web pages are brand new and have no precedents in the whole history of mathematics, and I think that math historians should cogitate on such a crude fact. Be sure that mathhistorians know that these methods have no precedents and cannot by any means deny such CRUDE TRUTH.
That is all what I said in all my posting to many groups and listings.
You assert that I have said: "I can solve the cube version of Pell's equation", and you are forcing me to ask you to show such a link to a posting from mine contining such phrase. All that i have said is that the methods shown in my webpages certainly produce best approximations and can yield high order convergence speed as shown in the very simple example on the square root I posted to you.
You showed Hurtwitz'S method pretending to state that such method is the same thing that I published in my webpages, and that is a FALSE STATEMENT FROM YOURS, so I compelled you to show YOUR ALLEGED HURTWITZ'S METHOD in order to prove to the sci.math audience that all what you were pretending to state about my methods is completely FALSE. You have made FALSE STATEMENTS ABOUT MY METHODS PRETENDING TO SAY THAT THEY ARE THE HURTWITZ'S METHOD AND THAT IS COMPLETELY FALSE AND YOU MUST RECOGNIZE THAT BECAUSE THERE CERTAINLY EXIST ETHICS. Worst, I have proved with concrete evidences that Hurtwitz's is not the originator of your alleged veryslow Hurtwitz's method as you also pretended to state. I proved that from the historical evidences JOHN WALLIS was one of the first mathematicians who used the MEDIANT (HE DID NOT USED THE RATIONAL MEAN, HE ONLY USED THE MEDIANT)
I have been so patience with you, even when you have shown that you are not willing to read any single bit of my webpages.
So I am including my last message to you below, and be sure I WILL NOT RESPOND ANY OTHER MESSAGE FROM YOU BUT WITH THE SAME MESSAGE THAT FOLLOWS:
********************************************************************** What could be strange for some people is that you are not willing to READ any single bit of my webpages. However, this is not strange to me, at all, that is the standard reaction to my critics on the whole history of rootsolving. That is the reason I have no intentions of sending any of these new and simple methods to any peer review journal, it is clear that they will not allow me to express all those critics against the mathematics we have inherited. They will not read any single bit of my methods in the same way as many others like you do.
The table of values you have posted IS NOT Hurtwitz's method, that is, Hurtwitz WAS NOT the author of such method as you have negligently alleged. That is a FALSE statement from yours.
The late mathematician David Fowler had the theory that Ancient Greeks used the Mediant to do things like the table you have posted, but there are no concrete evidences for his theory but just probable signs.
According to concrete evidences John Wallis certainly WAS THE AUTHOR of the method you have shown. Personally I would never assign the word "method" to such primitive trial&error algorithm which by the way, is the slowest algorithm you can find to compute anything. So it is so ridicule your intention of comparing such primitive and slow trial&error algorithm with the natural highorder arithmetical methods shown in my book and webpages.
I say "trial&error" because in each step of the "method" you need to know if your approximations are lower or higher (in this way you use: x^52y^5) than the true value of the root. Wallis used that way of operating mediants and got approximations to number 'PI'. Nicholas Chuquet also worked in a similar way the mediants but he improved the method by using unit fractions. There are others from past times who worked in such a primiteve way. All that is fully explained in my book and briefly mentioned in my webpages.
But... All that has nothing to do with my extremely simple HighOrder Arithmetical methods which do not need to make any trial&error checkings, and you know that, but my critics to the whole history of rootsolving really hurt you and you are not willing even to read any single bit of my webpages.
Well, I am sorry for that, but I will continue doing so because that is the CRUDE TRUTH, mathematicians of ancient times could have easily used Newton's, Halley's, Householder's methods by agency of the most simple arithmetic as shown in my book and webpages, however, they didn't. that is a real shame, worst when considering that the root solving issue is the very spine of the whole history of mathematics. I showed to you in this thread a TRIVIAL method based on the Rational Mean to find all the Householder's iterative functions for computing the square root and urged you to ask to your math teachers the reasons they didn't taught you such trivial stuff. Have you asked your teachers why they didn't taught you such trivial stuff at school? Of course, not, because you are not willing even to read any single bit of the square root sample I posted to you and the sci.math audience in this thread.
The very important question here is that: Why math teachers didn't taught you such trivial stuff at school?
Why?
The answer is very simple: Because they didn't know about the new methods shown at: http://mipagina.cantv.net/arithmetic/rmdef.htm
And it is striking to realize that math teachers didn't know about these trivial methods since Babylonian times up to now. Just striking.
> Can you solve x^3 2x^2 x+1 =0 ?
If you want to apply the highorder rootsolving methods shown in my webpages and book, for solving algebraic equations then I suggest you to look at (as well as my book):
MATHEMATICAL SPECTRUM. Bob Bertuello. The Rational Mean. Vol. 39, No. 2, 2006/2007. UK. An example on solving a polynomial equation by agency of the Rational Mean.
The author of the article used some of my methods to solve polynomial equations.
A link showing such reference appears at: http://mipagina.cantv.net/arithmetic
Of course, it is clear you have never visited any single bit of my webpages.
> Why is it that I can apply your method to simultaneously > approximate cubrt(2), cubrt(4) but you can't. ? Ocultar texto de la cita 
You have not tried anything, you have not even read any single bit of the methods shown in my webpages. You do not have purchased my book. You have not even take a look at the links and references shown at: http://mipagina.cantv.net/arithmetic
And you are not interested, at all, in developing anything related to the methods shown in my webpages. That is fairly clear to me and the sci.math audience.
You are just reacting to my hard critics to the history of mathematics which you seems to admire so much. Sorry for that, I do not admire the mathematics we have inherited. This statement from yours is as false as all the other statements you have posted in this thread, I mean, all your allegations on the Hurtwitz being the author of using mediants to find roots and your attempts to falsely state that my methods are the same as the one you negligently attibuted to Hurtwitz.
You have responded to my second challenge with a false statement on Hurtwitz's method and its nonexistent connection to my methods. I have shown you that Hurtwitz IS NOT the author, and that such primitive trial&error method is by far related to the methods shown in my webpages. All what you have said about your alleged Hurtwitz's method cannot be considered as a response to a challenge but just a very bad joke from yours, sci.math is not a place for joking but for doing mathematics.
So it is clear you have an X on the second challenge.
There are other false statements to have attibuted to me in this thread, but I am waiting for the response of you and your friend Grover Hughes to my first challenge:
My first challenge to you and your friend Grover Hughes was:
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).
You replied to Grover Hughes and endorsed his comments, so considering that he is absolutely unable to prove that my methods are the same that his alleged Eshbach's method, then you have to face your crude negligence on this matter. It is not my fault, it is your fault for being so negligent on this matter and reacting that way to my hard hard critics on the history of rootsolving.
In response to your mentioning the word "square root" I showed to you in this thread an extremely TRIVIAL method based on the Rational Mean to find all the Householder's iterative functions for computing the square root and urged you to ask to your math teachers the reasons they didn't taught you such trivial stuff. You have not responded anything on that.
I am not joking, I am very serious on this matter, because our young students deserve so much respect and a true mathematics, a true natural science.
I will not answer any other questions from you and your friend Grover Hughes till both challenges have been answered to me and the sci.math audience.
Ing. Domingo Gomez Morin Structural Engineer Caracas Venezuela

