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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 24, 2007 10:36 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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 root-solving 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 UNBIASED-MATHEMATICS 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 HIGH-ORDER 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 well-known Newton's, Bernoulli's, Halley's,
Householder's methods as well
as MANY OTHER new iterating root-solving 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 well-known 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 high-order 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 math-teachers 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 well-known Newton's, Bernoulli's, Halley's,
Householder's methods as well
as MANY OTHER new iterating root-solving 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 "well-defined 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 HIGH-ORDER ROOT-SOLVING
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 math-historians
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 very-slow 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 root-solving. 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 high-order
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^5-2y^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 High-Order
Arithmetical methods which do not need to make any trial-&-error
checkings, and you know that, but my critics to the whole history
of root-solving 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 high-order root-solving 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 non-existent 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
root-solving.


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































Date Subject Author
4/20/04
Read cube root of a given number
vsvasan
4/20/04
Read Re: cube root of a given number
A N Niel
4/20/04
Read Re: cube root of a given number
Richard Mathar
7/14/07
Read Re: cube root of a given number
Sheila
7/14/07
Read Re: cube root of a given number
amzoti
7/14/07
Read Re: cube root of a given number
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7/14/07
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arithmeticae
7/16/07
Read Re: cube root of a given number
Gottfried Helms
7/16/07
Read Re: cube root of a given number
Iain Davidson
7/21/07
Read Re: cube root of a given number
arithmetic
7/21/07
Read Re: cube root of a given number
arithmetic
7/21/07
Read Re: cube root of a given number
Iain Davidson
7/21/07
Read Re: cube root of a given number
arithmetic
7/22/07
Read Re: cube root of a given number
Iain Davidson
7/22/07
Read Re: cube root of a given number
arithmetic
7/22/07
Read Re: cube root of a given number
Iain Davidson
7/23/07
Read Re: cube root of a given number
arithmetic
7/24/07
Read Re: cube root of a given number
Iain Davidson
7/24/07
Read Re: cube root of a given number
arithmetic
7/24/07
Read Re: cube root of a given number
arithmetic
7/24/07
Read Re: cube root of a given number
Iain Davidson
7/25/07
Read Re: cube root of a given number
arithmetic
7/24/07
Read Re: cube root of a given number
gwh
7/25/07
Read Re: cube root of a given number
arithmetic
7/25/07
Read Re: cube root of a given number
Iain Davidson
7/25/07
Read Re: cube root of a given number
arithmetic
7/25/07
Read Re: cube root of a given number
Iain Davidson
7/25/07
Read Re: cube root of a given number
arithmetic
7/25/07
Read Re: cube root of a given number
arithmetic
7/25/07
Read Re: cube root of a given number
Iain Davidson
7/25/07
Read Re: cube root of a given number
arithmetic
7/26/07
Read Re: cube root of a given number
Iain Davidson
7/26/07
Read Re: cube root of a given number
arithmetic
7/26/07
Read Re: cube root of a given number
Iain Davidson
7/26/07
Read Re: cube root of a given number
arithmetic
8/6/07
Read Re: cube root of a given number
arithmetic
7/26/07
Read Re: cube root of a given number
semiopen
7/26/07
Read Re: cube root of a given number
Iain Davidson
7/26/07
Read Re: cube root of a given number
semiopen
7/26/07
Read Re: cube root of a given number
arithmetic
7/26/07
Read Re: cube root of a given number
semiopen
7/26/07
Read Re: cube root of a given number
arithmetic
7/26/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
Iain Davidson
7/28/07
Read Re: cube root of a given number
arithmetic
7/28/07
Read Re: cube root of a given number
Iain Davidson
8/5/07
Read Re: cube root of a given number
arithmeticae
8/5/07
Read Re: cube root of a given number
Iain Davidson
8/6/07
Read Re: cube root of a given number
arithmetic
8/6/07
Read Re: cube root of a given number
Iain Davidson
8/6/07
Read Re: cube root of a given number
arithmeticae
8/7/07
Read Re: cube root of a given number
Iain Davidson
8/7/07
Read Re: cube root of a given number
mike3
8/10/07
Read Re: cube root of a given number
arithmetic
8/10/07
Read Re: cube root of a given number
Iain Davidson
8/11/07
Read Re: cube root of a given number
r3769@aol.com
8/11/07
Read Re: cube root of a given number
Iain Davidson
8/11/07
Read Re: cube root of a given number
r3769@aol.com
8/11/07
Read Re: cube root of a given number
Iain Davidson
8/11/07
Read Re: cube root of a given number
r3769@aol.com
8/12/07
Read Re: cube root of a given number
Iain Davidson
8/17/07
Read Re: cube root of a given number
r3769@aol.com
8/12/07
Read Re: cube root of a given number
arithmetic
8/13/07
Read Re: cube root of a given number
Iain Davidson
8/24/07
Read Re: cube root of a given number
arithmetic
8/28/07
Read Re: cube root of a given number
narasimham
1/10/13
Read Re: cube root of a given number ...
Milo Gardner
8/28/07
Read Re: cube root of a given number
arithmetic
8/28/07
Read Re: cube root of a given number
Iain Davidson
8/7/07
Read Re: cube root of a given number
mike3
8/7/07
Read Re: cube root of a given number
Iain Davidson
8/10/07
Read Re: cube root of a given number
arithmetic
8/10/07
Read Re: cube root of a given number
arithmetic
7/28/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
arithmetic
7/27/07
Read Re: cube root of a given number
arithmetic
7/26/07
Read Re: cube root of a given number
Iain Davidson
7/26/07
Read Re: cube root of a given number
arithmetic
7/25/07
Read Re: cube root of a given number
Iain Davidson
7/26/07
Read Re: cube root of a given number
arithmetic
7/22/07
Read Re: cube root of a given number
arithmetic
7/21/07
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arithmetic
7/16/07
Read Re: cube root of a given number
Proginoskes
7/21/07
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arithmetic
7/22/07
Read Re: cube root of a given number
Proginoskes
7/22/07
Read Re: cube root of a given number
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7/22/07
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Proginoskes
7/23/07
Read Re: cube root of a given number
arithmetic
7/23/07
Read Re: cube root of a given number
arithmetic
7/24/07
Read Re: cube root of a given number
Proginoskes
7/16/07
Read Re: cube root of a given number
gwh
7/17/07
Read Re: cube root of a given number
Iain Davidson
7/21/07
Read Re: cube root of a given number
arithmetic
7/21/07
Read Re: cube root of a given number
arithmetic
7/21/07
Read Re: cube root of a given number
arithmetic
7/24/07
Read Re: cube root of a given number
pomerado@hotmail.com
7/25/07
Read Re: cube root of a given number
orangatang1@googlemail.com

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