Re: cube root of a given number
Sheila
quasi
<sheila_s...@sbcglobal.net> wrote:
>I would like to obtain this information.
Post the number you want the cube root of.
We charge 25 cents per cube root.
If not rational, standard is 10 decimal places. For more decimal
places, the price is higher. Inquire if needed.
quasi
amzoti
> I would like to obtain this information.
By Hand: http://mathforum.org/library/drmath/view/52605.html
Algorithm: http://mathforum.org/library/drmath/view/52628.html
Mathematica: N[(x)^1/3, 1000]
Example N[2^(1/3),1000]
1.2599210498948731647672106072782283505702514647015079800819751121552996765139\
594837293965624362550941543102560356156652593990240406137372284591103042693552\
469606426166250009774745265654803068671854055186892458725167641993737096950983\
827831613991551293136953661839474634485765703031190958959847411059811629070535\
908164780114735213254847712978802422085820532579725266622026690056656081994715\
628176405060664826773572670419486207621442965694205079319172441480920448232840\
127470321964282081201905714188996459998317503801888689594202055922021154729973\
848802607363697417887792157984675099539630078260959624203483238660139857363433\
909737126527995991969968377913168168154428850279651529278107679714002040605674\
803938561251718357006907984996341976291474044834540269715476228513178020643878\
047649322579052898467085805286258130005429388560720609747223040631357234936458\
406575916916916727060124402896700001069081035313852902700415084232336239889386\
49678219414983802707295717681287900144574622714770234835715190551
Math Source: http://mathworld.wolfram.com/CubeRoot.html
I am not sure which you were looking for - but hope that I understood.
~A
arithmeticae
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
Regards,
Ing. Domingo Gomez Morin
Gottfried Helms
> 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.
Yes, I'd second that. It surprises me, that this method is
not more widely discussed. It is -at least- an amazing
approach in his simpliness and in its line of proceeding,
even if it should not be efficient.
Hope, it will make its way into some books, at least as
an annotation, or in journals/books which are dedicated
to recreational and surprising mathematics.
Gottfried
--
Gottfried Helms, Kassel
sttsc...@tesco.net
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.
Monkmeyer and Mahler have examined generalizations
of Farey fractions, essentially a higher order
"mediant" method, intended to produce best rational
simultaneous approximations to a set of irrationals.
Can Morin find best rational approximations
to cubrt(2), cubrt(4) with his methods ?
He has not been able to do so in the past.
Proginoskes
All I'm getting, when I click on the links on that page, are "Lo
sentimos, no existe una página en el web de mipagina.cantv.net que
coincida con su petición" messages, which look like "page not found"
errors to me (and my very small Spanish vocabulary).
--- Christopher Heckman
gwh
>
> 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.
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.
Regards,
Grover Hughes
sttsc...@tesco.net
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 ?
arithmonic
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.
Frankly, I had so many doubts about answering this response from
yours, because I cannot realize if your remarks are the cosnequence
of your ignorance on the methods shown in my webpages, or you just
want to disturb people and cause confusion by making false statements.
Whatever the case, your comments are nonsense.
You mentioned "Farey Fractions".
Do you know what you are talking about?
I have never used any "Farey Fractions" in any of my methods, so I
cannot understand why you are mentioning them as the center of the
issue. Farey Fractions have been restricted only to reduced fractions,
and they operate only between TWO
> Hurwitz wrote a paper "Ueber die Irrationalzahlen"
> in the 1890s which describes a "mediant" method based on Farey
> fractions that produces best rational approximations.
> Monkmeyer and Mahler have examined generalizations
> of Farey fractions, essentially a higher order
> "mediant" method, intended to produce best rational
> simultaneous approximations to a set of irrationals.
> Can Morin find best rational approximations
> to cubrt(2), cubrt(4) with his methods ?
> He has not been able to do so in the past.- Ocultar texto de la cita -
>
> - Mostrar texto de la cita -
arithmonic
> 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.
Frankly, I had so many doubts about answering this response from
yours, because I cannot realize if your remarks are the consequence
of your ignorance on the methods shown in my webpages, or you just
want to disturb people and cause confusion by making false
statements.
Whatever the case, your comments are nonsense.
You mentioned "Farey Fractions".
Do you know what you are talking about?
I have never used any "Farey Fractions" in any of my methods, so I
cannot understand why you are mentioning them as the center of the
issue. Farey Fractions have been restricted only to reduced
fractions,
and they operate only between TWO FRACTIONS (even when you can compute
many Mediants at the same time it always operate between TWO
FRACTIONS). I cannot believe you dare
to talk about this issue without even reading any single bit of my
methods based on
the Rational Mean which is not restricted to reduced fractions and
operate on any set
of fractions.
> Hurwitz wrote a paper "Ueber die Irrationalzahlen"
> in the 1890s which describes a "mediant" method based on Farey
> fractions that produces best rational approximations.
The paper you are mentioning deals only with best approximations to
any given number, but that is far from being a ROOT-SOLVING ALGORITHM.
You are not bringing any reference to a ROOT-SOLVING ALGORITHM by far
similar to those shown in my web pages, worst, you are not bringing,
at all, any reference to any ROOT-SOLVING ALGORITHM. So, it is clear
that you don't know what you are talking about.
The issue on "best approximations" is well explained on my web pages.
It is well known that the fundamental law for generating the
convergents of continued fractions
is the "Mediant" which is the operation which rules Farey Fractions.
The fact that the Mediant is a particular case of the Rational Mean
does not mean nothing. All those well-known methods for finding best
rational approximations that you metined are basically "Continued
Fractions of the second degree" (all this is fully defined and
explained in my webpages, but it is clear that you have not read any
single bit of it)
Indeed, I cannot believe you dare to talk about all this without
taking care of what you read and say.
Indeed, it seems you even have not read any single bit of my webpages.
The only reason I can find for your making false statements and
causing confusion is that my comments about the whole root-solving
story really hurt you. I'm so sorry for that, but I have to continue
doing so, because all that is the crude Truth: It is strinking to
realize that such simple and trivial methods do not appear in any book
on numbers since Babylonian times up to now. I know that can really
hurt some people so much, sorry for that.
> Monkmeyer and Mahler have examined generalizations
> of Farey fractions, essentially a higher order
> "mediant" method, intended to produce best rational
> simultaneous approximations to a set of irrationals.
Again: You are referring to best approximations to any ginven number,
those mathematicians you mentioned didn't make any ROOT-SOLVING
METHOD. To find best approximations to any given number is far from
being similar to a GENERAL ROOT-SOLVING METHOD.
> Can Morin find best rational approximations
> to cubrt(2), cubrt(4) with his methods ?
YES, by means of these so TRIVIAL methods everybody CAN, even young
students at secondary schools.
It is finally clear that you have never read any single bit of my web
pages.
These new methods based on the Rational Means embrace --apart from
many other new algorithms--
all the well known Bernoulli's, Newton's, Halley's, Householder's
methods.
Many examples are shown in my web pages, you can compute any root of
any number with any convergence speed.
The examples are shown in my webpages, do not ask me to explain all
them here, just read them.
Your statements are the main reason for the title of my posting:
"DEDICATED TO YOUNG MATH STUDENTS..."
mainly because young people are usually eager to find new things and
try to read before talking about any issue, young people do not
pretend to be "experts" but just to learn and to think and that is
really wonderful, that is a virtue that many others have lost trough
the years that have them passed by.
> He has not been able to do so in the past.- Ocultar texto de la cita -
>
That's not true. Again it is finally clear that you have never read
any single bit of my web pages.
The only reason I can find for your making false statements and
causing confusion is that my comments about the whole root-solving
story really hurt you. I'm so sorry for that, but I have to continue
doing so, because all that is the crude Truth: It is strinking to
realize that such simple and trivial methods do not appear in any book
on numbers since Babylonian times up to now. I know that can really
hurt some people so much, sorry for that.
arithmonic
At the moment I am replying your posting the link is working properly.
http://mipagina.cantv.net/arithmetic/rmdef.htm
Try again, please, if you want to do so. Please, let me know if you
can not link to the page.
Some weeks ago CANTV.NET server had some problems, but by this moment
averything seems to be right.
arithmonic
You said:
>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.
Well, this is so simple. You are trying to say that my methods --based
on the Rational Mean-- are the same as the one you read in Eshbach's
work.
Well, I tell you that what you are stating is NOT true.
I challenge you to show such Eshbach's method in this thread.
This a challenge, and you must show people that all what you are
talking is true, otherwise,
you will face the consequences of making false statements.
I face all my statements. Can you?
Best regards.
Ing. Domingo Gomez Morin.
Caracas
Venezuela
arithmonic
wrote:
CORRECTION:
You can find TRIAL-&-ERROR methods based basically on Geometry, but
you will never
find SIMPLE AND NATURAL ARITHMETICAL METHODS based only on number
itself as those shown
in my webpages, and that is a HUGE difference.
Moreover, those old TRIAL-&-ERROR methods you mentioned worked
properly for square roots,
however, when dealing with higher roots all of them were just
PRECOMPUTING NIGHTMARES.
For not to mention that my methods hold high convergence speed (as
desired), which is something
that you cannot say about all those PRECOMPUTING NIGHTMARES you
mentioned.
Indeed, I think you really don't know what you are talking about, for
sure.
The issue on those old and well-known root-solving methods is fully
explained in my webpages, and
many comparisons are shown in my book and webpage.
That's the reason my posting was entitled "DEDICATED TO YOUNG MATH
STUDENTS". Some people
is not willing even to read any single bit of some new stuff, they
just care about themselves. Fortunatedly youngs are another very
different thing.
When I mention the word "Young" I am not referring to the word "AGE",
I am just referring to "Mental State"
sttsc...@tesco.net
> On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> 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.
>
>
> You mentioned "Farey Fractions".
> Do you know what you are talking about?
> many Mediants at the same time it always operate between TWO
> FRACTIONS).
Again you reveal your profound ignorance in these
matters. If you had read Hurwitz's paper you would
realize that you can generalize Farey fractions to
simultaneously approximate two irrationals, this
involves either double or triple mediants.
> The paper you are mentioning deals only with best approximations to
> any given number, but that is far from being a ROOT-SOLVING ALGORITHM.
If you approximate sqrt(2) you are solving x^2-2 =0
> The issue on "best approximations" is well explained on my web pages.
Then find the best simultaneous approximations to
cubrt(25), cubrt(625).
I've made this simple challenge many times in the past
and you were never able to meet it.
How can anyone believe what you say, if your
methods cam't produce what you claim.
arithmonic
You certainly know what you are talking about because it is clear that
you have read
so much about the whole history of mathematics, and that make all this
issue so easy
for you.
I know that the reason for some people to make fierce oposition
against these
methods and try to cause confusion, is mainly due to the fact that my
critics on the whole root-solving story really hurt many math
historians. I'm so sorry for that, but I will continue by doing so.
The crude Truth is that it is striking to realize that such simple and
trivial methods do not appear in any book on numbers since Babylonian
times up to now, and this really hurts.
Be sure that some math-historians really wished to prevent people from
reading my webpages, and that
is the main reason you will not see these methods in any Journal on
the History of Mathematics, and be sure, that I have no intentions of
sending any single bit of these methods to any of them
Many thanks for all you clever comments on this matter.
Be sure that these methods will find their way all through Young
minds, there is no way that some
mathematicians could ever prevent people from knowing about all this,
I have no doubts about that.
Be sure, that in a non-distant future every single young student will
be enjoying this new math, and it is for sure that many of them will
create many new wonderful things based on the Rational Mean.
Warmest regards,
Respectfully,
Domingo Gomez Morin
Civil Engineer
Structural Engineer
Caracas
Venezuela
arithmonic
wrote:
> On 21 Jul, 21:38, arithmonic <djes...@gmail.com> wrote:
>
> > On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> > 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.
>
> .
>
> > You mentioned "Farey Fractions".
> > Do you know what you are talking about?
> > and they operate only between TWO FRACTIONS (even when you can compute
> > many Mediants at the same time it always operate between TWO
> > FRACTIONS).
>
> Again you reveal your profound ignorance in these
> matters. If you had read Hurwitz's paper you would
> realize that you can generalize Farey fractions to
> simultaneously approximate two irrationals, this
> involves either double or triple mediants.
AGAIN: My webpages and book deal with methods for APPROXIMATING ROOTS
OF ANY DEGREE OF ANY POSITIVE NUMBER WITH ANY DESIRED CONVERGENCE
SPEED which certainly produce best approximations, But you do not want
to hear that, you just want to talk about simultaneous approximations
of two irrational numbers by means Farey Fractions.
You are talking about methods of finding best rational approximations
to any
given number, in the same way as anyone could do by using Continued
Fractions.
All those methods on best approximations using Farey Fractions are
basically just the
same thing than computing Continued Fractions of second order (as
explained in my web pages).
Let me put it clear to you and the sci.math audience:
I challenge you to show to the sci.math audience a very simple
arithmetical example on your
alleged Hurwitz's method for computing, say, THE FIFHT ROOT OF 2.
Just the FIFHT ROOT OF 2.
Come on, show to the audience such a simple example on Hurtwitz
method. Come on. Do not forget
not to mention anything related to Continued Fractions.
Hurtwitz DID NOT FIND ANY GENERAL ROOT-SOLVING METHOD AND YOU KNOW
THAT, but you
just want to cause confusion.
Every body knows that so many people have worked with Farey Fractions
that way, not only Hurtwitz but
many others, the math journals are plenty of articles on working with
Farey Fractions.
HOWEVER, to your disgrace, I DO NOT work with Farey Fractions. I do
not work with the Mediant and I got not only Newton's, Bernoulli's,
Halley's, Householder's methods but many other new algorithms with
high convergence speed which can be extende to algebraic equations.
YOU CERTAINLY KNOW that all that is far beyond the limited scope of
all your statements, some numerical examples are in my webpages and to
your disgrace you CAN NOT PREVENT PEOPLE FROM READING THEM. ALL THOSE
NEW METHODS HAVE NO PRECEDENTS, AT ALL, and you cannot deny that.
> > The paper you are mentioning deals only with best approximations to
> > any given number, but that is far from being a ROOT-SOLVING ALGORITHM.
>
> If you approximate sqrt(2) you are solving x^2-2 =0
No, you are wrong, Hurtwitz DID NOT find any NEW GENERAL ROOT-SOLVING
METHODS he was basically
working the same thing that has been known since long time ago as
CONTINUED FRACTIONS,
that is, those things I use to call Continued Fractions of Second
Degree, because there are
Continued Fractions of Higher degrees.
I challenge you to show to the sci.math audience a very simple
arithmetical example on your
alleged Hurwitz's method for computing, say, THE FIFHT ROOT OF 2.
Just the FIFHT ROOT OF 2.
Come on, show to the audience such a simple example on Hurtwitz
method. Come on. Do not forget
not to mention anything related to Continued Fractions.
>
> > The issue on "best approximations" is well explained on my web pages.
>
> Then find the best simultaneous approximations to
> cubrt(25), cubrt(625).
>
> I've made this simple challenge many times in the past
> and you were never able to meet it.
I really do not remember to have discussed with you any single line,
if you have addressed any message to me in the past be sure it did
not arrive at my end.
Anyway, I can only say is: read my webpages, and compute all the roots
you want and find all the best approximations you desire.
My webpages deal exclusively with EXTREMELY SIMPLE ROOT-SOLVING
METHODS WHICH DO NOT APPEAR IN NEITHER ANY CHINESE, NOR EUROPEAN, NOR
ARAB, NOR HINDU, NOR AMERICAN BOOK ON NUMBERS, since Babylonian times
up to now, and you are trying to cause confusion by challenging me to
solve the cube version of Pell's equation.
No, you are wrong, what you see in my postings, my webpages and book
is what you get. You are the only one who insists to talk about any
simultaneous approximations by agency of Farey Fractions, but
my work is about: NEW EXTREMELY SIMPLE ROOT-SOLVING METHODS WHICH
SURPRISINGLY DO NOT APPEAR IN NEITHER ANY CHINESE, NOR EUROPEAN, NOR
ARAB, NOR HINDU, NOR AMERICAN BOOK ON NUMBERS, since Babylonian times
up to now. My point has been stated very clear, and be sure that I
will not allow
any strategy from yours to divert that.
NOW, you are trying to introduce much more confusion by challenging me
to solve the cube-version of Pell's equation.
YOU ARE WRONG, I challenged to you and your friend Grover Hughes to
ask the following issues:
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).
2.- I challenged you in this posting to show to the sci.math audience
a very simple numerical example on your alleged GENERAL Hurwitz's
ROOT-SOLVING METHOD for computing, say, THE FIFHT ROOT OF 2.
You have made very specific statements about my methods and I am
challenging you to prove them by
means of very concrete evidence.
Notice that I am challenging you and your friend Grover Hughes with
two very simple inquires.
If none of you is able to ask such simple challenges then both of you
will have to face the conseequences of your negligence.
arithmonic
Both you and I certainly know that you will not answer to my simple
challenge, i mean, to show any
simple numerical example on Eschbach's method, so sci.math audience
could be able to realize that you are telling the truth, mainly
because you certainly know that the new simple arithmetical methods
shown in my webpages and book have no precedents, at all.
However, I will do a favor to you and your friend
sttsc...@tesco.net. Yes I will
show to you a very simple example on computing square roots by agency
of the RATIONAL MEAN (notice
that i am not talking about NEITHER FAREY FRACTIONS NOR PELL'S
EQUATION)
THE VERY SIMPLE EXAMPLE FOLLOWS. I am sure you will also be able to
say that you have read
what follows in so many books on numbers (PUN INTENDED, OF COURSE),
worst when considering
that we are talking at this moment about SIMPLE SQUARE ROOTS:
All this comments comes from the contents of the webpage:
http://mipagina.cantv.net/arithmetic/rmdef.htm
and the book: LA QUINTA OPERACIÓN ARITMÉTICA. Arithmonic Mean. ©
Domingo Gomez Morin. Copyright. All rights reserved. 2006
-----------------------------------PRELIMINARY
NOTE-----------------------------------
The Rational Mean of the fractions: f1=a1/b1 and f2=a2/b2 is:
Rm[f1, f2] = (a1+a2)/(b1+b2)
By agency of such a simple arithmetical operation you can produce all
the Householder expressions for the Nth root of any number P.
Notice that if you change the form of the fraction a1/b1= (x/x)*(a1/
b1)= (x*a1)/(x*b1) then you will get another result (provided that x
is not equal to 1):
For example: Rm[(x/x)*f1, f2]= (x*a1 + a2) / (x*b1 + b2)
--------------------------------END OF
NOTE----------------------------------------
Higher-order rational process based on the Rational Mean:
FUNDAMENTAL PRINCIPLE:
Any two fractions whose product is P represent two rational
approximations -by defect and excess-- to the square root of P.
If departing from those two fractions you can compute two mean values
whose product is also P then you have another two closer
approximations to the root. By continuing this process you will get a
root-solving algorithm for the square root of P, moreover, by using
the Rational Mean you will get a higher-order root-solving algorithm.
Starting with a set of two fractions f1, f2 whose product is f1*f2 =
P.
For example:
f1 =x/1 f2=P/x
Compute the following two rational means:
Rm[(x/x)*f1, f2] = (P+x^2) / (2x) (Newton)
Rm [(P/P)*f1, (x/x)*f2]= (2Px) / (P+x^2)
It yields, two expressions whose product is trivial and equal to P
and are closer to the square root of P.
You can use each of those new functions as independent iterating
functions both of them converging quadratically.
If you don't like quadratic convergence then compute another two
similar rational means by previously assigning those new functions to
f1 and f2, as follows:
f1 = (P+x^2) / (2x)
f2 = (2Px) / (P+x^2)
The two new rational means yields:
Rm [(x/x)*f1, f2] = (x^3 + 3Px) / (P
+3x^2) (Halley)
Rm [(P/P)*f1, (x/x)*f2]= (P^2 + 3Px^2) / (x^3 + 3Px)
two expressions whose product is trivial and equal to P, both of them
multiply by THREE the number of exact digits in each iteration.
If you prefer more convergence speed, then make:
f1 = (x^3 + 3Px) / (P+3x^2)
f2 = (P^2 + 3Px^2) / (x^3 + 3Px)
and compute other two rational means:
Rm [(x/x)*f1, f2] = (x^4 + 6Px^2 + P^2) / (4x^3 + 4Px)
(Householder)
Rm [(P/P)*f1, (x/x)*f2]= (4Px^3 + 4xP^2)/ (x^3 + 3Px)
Two expressions whose product is trivial and equal to P, both of them
multiply by FOUR the number of exact digits in each iteration.
By continuing this process, in the next step you will get two
functions which multiply by five the number of exact digits in each
iteration.
And so on.
Believe it or Not!.
Based on the evidence at hand, this so naïve, trivial, natural and
simple rational process has no precedents since Sumerians times up to
now. We have not used neither any Cartesian-decimal system, nor any
derivatives, nor infinitesimal calculus, at all
I think, many experts on the history of mathematics should cogitate on
the very long story on root-solving. Indeed, it is disturbing to
realize these so simple rational processes based on the rational mean
do not appear in any book on numbers since ancient times up to now.
All this is fully explained in my book:
LA QUINTA OPERACIÓN ARITMÉTICA. Arithmonic Mean © Domingo Gomez Morin.
Copyright. All rights reserved. 2006
and its webpage:
http://mipagina.cantv.net/arithmetic
arithmonic
Did you dare to mention SQUARE ROOTS when talking about your alleged
GENERAL HURTWITZ's ROOT-SOLVING METHOD? (pun intended)
Very funny, indeed.
please , do a favor to the sci.math audience, ask to HURTWIZT to tell
you if by means of FAREY FRACTIONS he pubished something similar to
all what follows. I am sure you have the cheek to say that you have
read all what follows in many books on numbers, even in ancient clay
tablets. (Pun intended)
Of Course this challenge apply also to your friend.
Wait a minute, please do not tell me that your math teacher and even
HURTWITZ never told you anything about what follows. What a shame,
indeed, worst when considering that I am only bringing to you a
TRIVIAL EXAMPLE ON SQUARE ROOTS. What a shame, indeed.
Notice, that what follows is neither about Farey Fractions, nor
Continued Fractions, nor Pell's equation, nor pigeon holes, nor birds,
nor cows, but just about a simple example on the GENERAL ROOT SOLVING
METHODS shown in my book and webpages, such methods have no precedents
in the whole history of mathematics and certainly yields best
approximations. Could you ever understand or accept that? i do not
think so, because this hurts so much, indeed, and I understand you,
and i DON'T care, and I will continue spreading this CRUDE TRUTH, and
you will not be able to prevent people from reading all this.
--------------------------------END OF
NOTE----------------------------------------
And so on...
That is, you will get all the Householder expressions for the square
root along with another iterating function.
Proginoskes
> On 16 jul, 17:18, Proginoskes <CCHeck...@gmail.com> wrote:
>
>
>
> > 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.
>
> > > Don't forget to take a look at the links and references:
> > >http://mipagina.cantv.net/arithmetic
>
> > All I'm getting, when I click on the links on that page, are "Lo
> > sentimos, no existe una página en el web de mipagina.cantv.net que
> > coincida con su petición" messages, which look like "page not found"
> > errors to me (and my very small Spanish vocabulary).
>
>
> http://mipagina.cantv.net/arithmetic/rmdef.htm
>
> Try again, please, if you want to do so. Please, let me know if you
> can not link to the page.
>
> Some weeks ago CANTV.NET server had some problems, but by this moment
> averything seems to be right.
Nope. Still not working.
--- Christopher Heckman
Virgil
Proginoskes <CCHe...@gmail.com> wrote:
> > At the moment I am replying your posting the link is working properly.
> >
> > http://mipagina.cantv.net/arithmetic/rmdef.htm
> >
> > Try again, please, if you want to do so. Please, let me know if you
> > can not link to the page.
> >
> > Some weeks ago CANTV.NET server had some problems, but by this moment
> > averything seems to be right.
>
> Nope. Still not working.
>
> --- Christopher Heckman
I connect quite rapidly to a page with title "The Rational Mean".
I am using MT-Newswatcher on an eMac to access newsgroups and Safari on
that same eMac to wander through the Web.
sttsc...@tesco.net
> On 21 jul, 17:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
>
> > On 21 Jul, 21:38, arithmonic <djes...@gmail.com> wrote:
>
> > > On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
>
> 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 knows what he read.
> 2.- I challenged you in this posting to show to the sci.math audience
> a very simple numerical example on your alleged GENERAL Hurwitz's
> ROOT-SOLVING METHOD for computing, say, THE FIFHT ROOT OF 2.
There are 5 fifth roots of 2. Which one do you want ?
Are you saying you can find complex roots too ?
Finding the real root of x^5-2 =0 is simple.
s(x,y) is the sign of binary quntic x^5-2y^5
The root must lie between (0,1) = 0 and (1,0) = "inf"
calculate s(0,1) and s(1,0). Form the mediant (1,1)
At any stage in the process s(xn,yn) will be 1 or -1.
if s(xn,yn) = un The new new mediant is formed with
(xk,yk) where k is the largest index <n such that un*uk = -1
0 1 -1
1 0 1
1 1 -1
2 1 1
3 2 1
4 3 1
5 4 1
6 5 1
7 6 1
8 7 -1
15 13 1
23 20 1
31 27 -1
54 47 1
85 74 -1
139 121 1
224 195 1
309 269 1
394 343 -1
703 612 -1
1012 881 -1
1321 1150 -1
1630 1419 -1
1939 1688 -1
2248 1957 -1
2557 2226 -1
2866 2495 -1
3175 2764 -1
3484 3033 -1
3793 3302 -1
4102 3571 -1
4411 3840 -1
4720 4109 -1
5029 4378 -1
5338 4647 -1
5647 4916 -1
5956 5185 -1
6265 5454 -1
6574 5723 -1
6883 5992 -1
7192 6261 -1
7501 6530 -1
7810 6799 -1
8119 7068 1
15929 13867 -1
24048 20935 -1
32167 28003 -1
40286 35071 -1
48405 42139 1
88691 77210 1
128977 112281 1
169263 147352 -1
298240 259633 -1
Can you solve x^3 -2x^2 -x+1 =0 ?
> Notice that I am challenging you and your friend Grover Hughes with two very simple inquires.
I don't know why you think Grover Hughes is a friend of mine.
You used to claim that you could find the best simultaneous
approximations to cubrt(2), cubrt(4).
As you methods are so revolutionary, I would have thought
this would have been possible too.
In fact, you can use your methods for simultaneous approximation of
cubrt(2), cubrt(4), but it would be
sheer luck if a best approximation was found.
Shall I give you a hint ?
Do you understand the diffference between fast convergence and best
rational approximation ?
arithmonic
wrote:
> On 22 Jul, 04:28, arithmonic <djes...@gmail.com> wrote:
>
> > On 21 jul, 17:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> > wrote:
>
> > > On 21 Jul, 21:38, arithmonic <djes...@gmail.com> wrote:
>
> > > > On 16 jul, 04:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
>
> > 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 knows what he read.
Why are you so sure? Are you his friend?
I am sure that the poster called Grover Hughes does not know a single
bit of all what he was talking about, tha's why I challenged him and
be sure the method he mentioned is by far similar to the methods shown
in my web pages. The sci.math audience is also waiting and observing
the results of my challenges to both of you.
Now to the very specific point on ROOTS-SOLVING METHODS:
One step at the time, please.
Let us focus on the main point of this thread: The extremely simple
high-order arithmetical methods shown in my webpages, and your
allegued Hurtwitz's Root-Solving Method as being the same thing that
my methods, in such a way, that when talking about them you stated: "I
don't think the claim that these methods are in any way new stands up
to scrutiny."
Only after clarifying this point to the sci.math audience I will
procede to answer all the other
remarks you have made in this posting.
But... Please, If you don't mind, I want to ask you just two more
questions specifically related to this table you have shown on the
fifth root and your remark about the methods shown in my webpages: "I
don't think the claim that these methods are in any way new stands up
to scrutiny."
ARE YOU JUST PLAYING A JOKE OR WHAT?
HAVE YOU EVER READ A BOOK ON THE HISTORY OF MATHEMATICS?
sttsc...@tesco.net
What I find strabge is that you claim to have invented
a new method of root solving and yet seem to be incapable
of applying it to any problem I pose.
Can you solve x^3 -2x^2 -x+1 =0 ?
Why is it that I can apply your method to simultaneously
approximate cubrt(2), cubrt(4) but you can't. ?
Proginoskes
> In article <1185078186.770779.45...@o61g2000hsh.googlegroups.com>,
>
> Proginoskes <CCHeck...@gmail.com> wrote:
> > > At the moment I am replying your posting the link is working properly.
>
> > >http://mipagina.cantv.net/arithmetic/rmdef.htm
>
> > > Try again, please, if you want to do so. Please, let me know if you
> > > can not link to the page.
>
> > > Some weeks ago CANTV.NET server had some problems, but by this moment
> > > averything seems to be right.
>
> > Nope. Still not working.
>
So do I. But when I click on the "New High-order Arithmetical Root-
Solving Algorithms" link, I get a 404 message.
--- Christopher Heckman
arithmonic
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.
arithmonic
>
> - Mostrar texto de la cita -- Ocultar texto de la cita -
>
> - Mostrar texto de la cita -
So sorry for that.
You are right.
Please, just look at the methods shown in that page, do not click that
link.
That is just and index link for the contents in that page.
Such link should not drive you to another page but to another point
in the same page,
however, it is not functioning properly. Sorry for that, I will fix it
as soon as I can.
Many thanks for letting me know.
Domingo Gomez Morin
Caracas
Venezuela
arithmonic
>
> - Mostrar texto de la cita -
I think the problem with the indexed-links is fixed.
So sorry for the trouble casued by the missed link within the page.
Thanks again fo letting me know.
Ing. Domingo Gomez Morin
Structural Engineer
Caracas Venezuela
Proginoskes
Yes, it seems to be working now.
--- Christopher Heckman
sttsc...@tesco.net
> On 22 jul, 20:38, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
>
> > On 22 Jul, 23:47, arithmonic <djes...@gmail.com> wrote:
>
> > > On 22 jul, 07:29, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> > > wrote:
>
> > > > On 22 Jul, 04:28, arithmonic <djes...@gmail.com> wrote:
>
> > > > > On 21 jul, 17:39, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> > > > > wrote:
> I DO NOT USE the MEDIANT.
The mediant of any two fractions a/b, c/d
is usually defined to be (a+c)/(b+d)
> The MEDIANT works only with reduced
It depends what you mean by "works"
3/5 = 6/10
2/3 = 10/15
5/8 <> 16/25
This just means that the interval between
the two fractions is being divided in different ratios.
If
a/b = pa/pb
c/d = qc/qd
(a+c)/(b+d)
(pa + qc)/(pb +qd)
divide the interval between the fractions
in different ratios.
This would not matter in your case as you are
neglecting the key property of Farey intervals
All you require is that the distance between the fractions
enclosing the irrational you want to approximate gets
smaller, i.e. the fractions get nearer the approximand.
The Farey mediant is defined on two consecutive elements
of a Farey sequence s/t, u/v with tu-sv =1.
This is essential to find best rational approximations.
as the Farey mediant is then the fraction with the smallest
denominator between s/t and u/v.
A Farey mediant is a mediant, and also a " rational mean"
in your terminology, but the converse isn't necessarily true
a mediant or " rational mean" does not have to
be a Farey mediant
Changing the name of (a+c)/(b+d) does not change its properties.
M(a/b,c/d)= (a+c)/(b+d) is not a well-defined binary operation.
even if you call it "moolyming"
This is simply a matter of common sense.
If M(2,5) = 6, then it would be reasonable to expect
that M(1+1,2+3) =M(4/2,15/3) =6.
It has nothing to do with the "Cartesian/decimal system"
whatever you mean by that term.
>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.
The Farey mediant is well-defined as is the reduced fraction
mediant but everyone expects OPERATIONS to be well-defined.
the "square operation" SQR(n) should return the same
result on identical numbers.
SQR(4) = SQR(2+2) = SQR(12/3).
I don't see that this matters fundamentally for your method.
The problem is purely linguistic. By using the words
"arithmetical operation" you are making a claim about
the "rational mean" which is clearly not true, because
"operation" means something quite specific in a mathematical
context.
The same problem may be occurring when you claim that
your method produces "best approximations"
p/q is a best approximation to sqrt(2), if there is no
other rational p'/q', q' <q closer to sqrt(2).
I know that your methods can't produce
best approximations because they do not use Farey
fractions. It is just chance if a best approximation is found.
It doesn't really matter whether your mediants are
in this sense well-defined or not.
The consequence of not using reduced fractions is that
the "rational mean" will not necessarily equal the Farey
mediant and some best approximations will be lost (best case)
or no best approximations will be found at all.
>I have never said that my using the Mediant or the Rational Mean is
> new.
This was not clear to me, but is now.
The mediant is not exactly a new concept.
>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)
Yes, the Farey mediant eventually gets you to continued fractions
which give "ultragood" rational approximations.
But your method does not do this. It is not based
on Farey mediants.
Continued fractions have very special properties. That is why
they have been studied so intensely.
Every convergent is an "ultragood" rational approximation
and they distinguish between rationals, quadratic irrationals and
higher irrationals.
Any "higher dimensional" generalization should produce "ultragood"
rational
approximations and, say, distinguish between
rationals, quadratic irrationals, cubic irrationals and higher
irrationals.
I mentioned x^3 +Ay^3 +AAz^3 -3Axyz = 1 because
it is a higher analogue of Pell's equation. If your
"higher order" methods prodiuce best approximations
they should be able to find solutions to the cubic Pell.
I have not seen you demonstrate this.
>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.
This is a historical claim and may well be true.
Although one poster has claimed to have found
this in a book published in 1945.
I don't know how you are going to search through
every book published since Babylonian times to
confirm your claim.
If mediant-based methods have been used
since the Middle Ages, it does not seem
implausible that your method is a rediscovery.
It is a common phenomenon.
>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
No, that they cannot do.
>and can yield high order convergence speed as shown in the very
>simple example on the square root I posted to you.
Yes, that may well be true.
You make at least two mathematical claims about
your method that are false. (arithmetical operation,
best approximations).
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
arithmonic
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, Platón,
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:
**********************************************************************
Why?
arithmonic
Marginal Note:
*************
Apart from the issue on the NEW high-order arithmetical Root-Solving
methods shown at:
http://mipagina.cantv.net/arithmetic/rmdef.htm
I think that I have realized why you insist so much in talking about
best approximations
and pell's equation.
Another webpage from mine show a brief description on new
"Generalized continued Fractions":
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
the esence of such new GCF is to show that one can easily construct
periodic representations of irrational numbers of higher degree tha 2,
i.e., periodic representations of non-quadratic roots.
In this way, if one try to represent the cube root of 2 by means of
the traditional continued fractions (Second order continued fractions
as we should call them) then one get a distorted representation (non-
periodic coefficients) of this irrational number. By means of these
new GCF
one can find periodic representation of irrational numbers of degrees
higher than 2.
Some time ago I posted some info on that webpage and it might be you
understood that I was claiming
to have solved the Cube version of Pell's equation.
Of course, I must say that the new ARITHMONC MEAN (shown in my
webpages) could be a very useful tool to study the issue on Cube
version of Pell's equation.
But your statement about that I claimed to have solved the cube Pell's
equation is another absolute FALSE STATEMENT from yours. Of couse I
always grant people a second chance, it might be that you
misunderstood all what I told about GFC or some other people
intentionally caused confusion
as it has been the habit for some people who try to prevent others
from looking at the
new methods shown in my webpages becasue of my critics to the whole
history of root-solving,
I really don't care, these simple methods will find their way all
through young minds,
and no one will be able to stop that. I do not look to get favors from
any peer-reviewed journal in exchange for not including my critics
against the history of root-solving.
My criticism on the history of root-solving will continue for so long
time.
Anyway, notice that I will not discuss GCF this thread, just take
this as a marginal note.
Ing. Domingo Gomez Morin
Caracas
Venezuela
http://mipagina.cantv.net/arithmetic
Richard Henry
> I would like to obtain this information.
<start> <all programs> <accessories> <calculator>
enter the number
<inv> <x^3>
sttsc...@tesco.net
> *************
> But your statement about that I claimed to have solved the cube Pell's
> equation is another absolute FALSE STATEMENT from yours.
No, you have obvuiosly forgotten, my comments on
your insane rantings some years ago.
You should be able to find them by searching for
Morin, Davidson, Pell.
You were also claiming that your methods could solve
the standard Pell equation. Claims which also
turned out to be wrong. You have never
admiited that you were wrong. But that would be too much
to expect.
gwh
> 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 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.
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. If anyone's interested, I'll be happy to scan the page
and email it directly to you-- just ask. Anyway, here's what page 2-04
of Handbook of Engineering Fundamentals", edited by Ovid . Eshbach,
copyright 1936 , gives, to find the cube root of 158252.632929 :
158 252. 632 929 |
54.09
5^3 = 125
_____
300 X 5^2 = 7500 | 33 252
30 X 5 X 4 = 600 |
4^2 = 16 |
_____|
8116 | 32 464
300 X 540^2=87480000 | 788 632 929
30 X 540 X 9= 145800 |
9^2 = 81 |
_________ |
87625881 | 788 632 929
I know that it would have been better had Eshbach chosen a number
which was not a perfect cube, but the method works fine for that case,
anyway--- I used it sometimes to check my slide rule value, for
greater precision....
Sorry about the clumsy presentation, but that's the best I know how to
type this stuff-- the lines above which are blank except for an
underline are supposed to appear directly under the 4^2 = 16
and 9^2 = 81
but I can't underline and type numbers at the same time. Is there a
way?
Eshbach of course gives a written explanation for each step, but to
save all of us time, I am assuming that everyone reading this is
perfectly capable of working that out for himself. If you do want the
entire text from Eshbach, lemme know and I'll either email it (as I
said earlier) or I'll type it out and post it here some day soon-- I
don't look at sci.math every day, just when I feel like it, so forgive
the time lapse. Write me directly if you wish, at ghu...@cei.net.
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
arithmonic
Now, I am free to respond to BOTH OF you as you deserve before the
sci.math audience because it has been proven that you and your friend
Grover Hughes were making just FALSE STATEMENTS.
Grover Hughes negligently wrote:
On 16 jul, 18:24, gwh <ghug...@cei.net> wrote:
> 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.
>
> 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.
and his friend also <sttscitr...@tesco.net> 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
All the two assertions from Grover Hughes and his friend
<sttscitr...@tesco.net> has been proven
to be absolutely FALSE and UNETHICAL STATEMENTS. Their allegued
Hurtwitz 's method (which in fact his originator was Achimedes or
Wallis if you prefer) and Eshbach's method are not by far the same
that 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 mantain 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 do think it 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 thing are we missing.
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.
On 24 jul, 12:41, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
Yes, in this newsgroup you and some others guys in the past tried to
do exactly the
same unethical acts than you and your friend Grover Hughes have tried
this time.
You got a cheek, indeed.
You and all your friends should cogitate on your unethical attitude.
In past times, You insisted to say that the methods shown in my
webpages do
not yield best approximations and I told you and again I tell you this
time that such methods certainly produce best approximations. The fact
that some of those methods based on the Rational Mean could not
produce ALL the best approximations is another problem which is the
same problem
with Newton's, Halley's, etc. when computing some particular roots.
I challenge you to show a posting from mine saying exactly what you
are attributing to me,
that is: "I can solve the cube version of Pell equation"
That is another FALSE STATEMENT FROM YOURS, as FALSE as all the other
statements that you
and your friend Grover Hughes pretended to state in order to prevent
people from reading my book and webpages. But you have failed again in
the same way that in past times you and others did.
You, your friend Grover Hughes and some others from past times have
had the same unethical attitude,
many of you use to form kind of packs and make all kind of FALSE
statements causing confusion and preventing people from reading one's
work. That's an unethical attitude.
But, you know? I don't care and I have never cared of such packs and
unethical attitude, because the methods shown in my webpages easily
demolish all such unethical attempts, and such trivial high-order
methods will remain there even after I have died out.
What I have always said is that my methods embrace Newton's,
Bernoulli's, Halley's, Househloder's
and many other NEW iterating functions for solving roots. My method is
not just one algorithm but
a new general and very simple concept involving so many high-order
methods.
The point these methods are based on the most simple arithmetic and
that is really striking mainly
when considering the very long story on root-solving.
The methods shown in my pages :
http://mipagina.cantv.net/arithmetic/rmdef.htm
DO CERTAINLY YIELD BEST APPROXIMATIONS, of course they CERTAINLY DO,
and I AM SURE that the NEW ARITHMONIC MEAN is the best tool to work
the cube version of PELL'S EQUATION, and that is all what I have ever
said.
IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC
MEAN PROCESSES SHOWN IN MY WEBPAGES. That hurt yours and some others
feelings (mainly math-historians) but that's not my fault,
ask mathematicians from past times why they didn't developed such
TRIVIAL HIGH-ORDER ARITHMETICAL NON-TRIAL-&-NON-ERROR ALGORITHMS.
I have no intentions of sending these NEW methods to any peer-review
journal, I don't need to give detailed explanations on why, I think my
reasons are very fairly clear.
I think this is matter of ETHICS, MORAL AND UN-BIASING MATHEMATICS.
If a math-historian take a look through all those new simple
arithmetical methods --based on the rational mean-- the such
mathematician must have the MORAL OBLIGATION to make comments and
include some analysis on them in his books, papers, etc. THAT JUST A
MATTER OF MORAL AND ETHICS, MAINLY WHEN CONSIDERING THE VERY LONG
STORY ON ROOT-SOLVING.
Ing. Domingo Gomez Morin
Caracas
Venezuela
http://mipagina.cantv.net/arithmetic/rmdef.htm
arithmonic
> 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 GOT A CHEEK, INDEED.
YOUR UNETHICAL ATTITUDE ONLY MATCH THAT FROM OTHERS IN THE PAST IN
THIS NEWGROUP.
EXACTLY THE SAME UNETHICAL ATTITUDE.
Now, I am free to respond to BOTH OF you as you deserve before the
sci.math audience because it has been proven that you and your friend
Grover Hughes were making just FALSE STATEMENTS.
Grover Hughes negligently wrote:
On 16 jul, 18:24, gwh <ghug...@cei.net> wrote:
> 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.
>
> 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.
and his friend also <sttscitr...@tesco.net> 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
All the two assertions from Grover Hughes and his friend
<sttscitr...@tesco.net> has been proven
to be absolutely FALSE and UNETHICAL STATEMENTS. Their allegued
Hurtwitz 's method (which in fact his originator was Achimedes or
Wallis if you prefer) and Eshbach's method are not by far the same
that 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 mantain 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 do think it 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.
sttsc...@tesco.net
>
> BTW, does arithmonic always get so excited and upset? I never intended
> to help his ulcer along......
lied and conspired to subvert his worldview - namely that
the mathematical world since Babylonian times has schemed to prevent
his "method" emerging
and that even today we (for you are my secret friend) and the
mathematical community are deliberately failing to understand his
valuable insights and voluminous rantings.
Unfortunately, the method you describe is not his.
But he would not have believed you, even if you
had found a reference.
El Morono simply does not understand that his
method is a trivial variant of Heron's method.
Basically, to find say the square root of 7, you
would start with a 1x7 rectangle. You want
to preserve the area but make the sides more and
more equal so you take the average of 1 and 7
(1+7)/2 = 4. This is one side of a new rectangle, the
other side is 7/4 =1.75. The area of the rectangle
is 7, but the sides are more equal.
All Morin does is represent the sides as fractions
(7/1, 1/1) and use the mediant as the averaging function.
(7+1)/(1+1) = 4/1. The other side is 7/(4/1) =7/4. The area
of the rectangle is preserved, the sides are more equal.
(4 +7)/(4+1) = 11/5 and so on.
He will never understand what a best rational approximation is.
sttsc...@tesco.net
> IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC
> MEAN PROCESSES SHOWN IN MY WEBPAGES.
Put your money where you enormous mouth is and
demonstrate how your method solves x^2 -69y^2=1
using the best rational approximations you can muster.
Or are you simply a grandiloquent windbag ?
arithmonic
wrote:
> > IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC
> > MEAN PROCESSES SHOWN IN MY WEBPAGES.
>
>
> Or are you simply a grandiloquent windbag ?
The sci.math audience can see that you have no choice but to insult,
you and your friend have shown an unethical attitude and you should
cogitate on that.
I have nothing more to add about the unethical attitude from you and
your friend.
Ask to Newton's , Halley's, etc. whatever you want to ask I have no
intentions to answer
any other question from you and your friend Grover Hughes.
If you think that you can make me upset, your are WRONG, so WRONG. I
do not look for any favors from
neither any intitution nor any peer-review journal. I really enjoy
what I am doing: TO TELL THE CREUDE TRUTH ABOUT THE WHOLE HISTORY OF
ROOT SOLVING.
I only regret that your so low self-esteem leads you to set such a
shameful example to young students. I regret that so much.
The simple high-order methods shown in my webpages have demolished
others in the past in the same way as they have done with both of you
(might be that some of you could be someone from the past,
whatever...I do not care).
So, from now on you will get the same message I gave to both of you
last time:
On 24 jul, 17:07, gwh <ghug...@cei.net> 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 GOT A CHEEK, INDEED.
YOUR UNETHICAL ATTITUDE ONLY MATCH THAT FROM OTHERS IN THE PAST IN
THIS NEWGROUP.
EXACTLY THE SAME UNETHICAL ATTITUDE.
WHAT FOLLOWS IS WHAT THIS GUY Grover Hughes RESPONDED TO MY ORIGINAL
MESSAGE:
Grover Hughes negligently and unethically wrote:
On 16 jul, 18:24, gwh <ghug...@cei.net> wrote:
> 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.
***********************************************************************************************
***********************************************************************************************
> 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.
***********************************************************************************************
***********************************************************************************************
AND WHAT FOLLOWS IS 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
All the two 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
that 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.
On 24 jul, 12:41, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC
sttsc...@tesco.net
> On 25 jul, 11:26, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
>
> > > IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC
> > > MEAN PROCESSES SHOWN IN MY WEBPAGES.
>
> [CUT]
>
> > Or are you simply a grandiloquent windbag ?
>
> The sci.math audience can see that you have no choice but to insult,
> you and your friend have shown an unethical attitude and you should
> cogitate on that.
You make unsubstantiated claims, based on your
bizarre imagings and expect to be believed without proof.
Instead of twittering endlessly like a broken record,
produce a rational case for your rather improbable claims.
Start your case with this challenge as you claim
your method produces best rational approximations.
Demonstrate how your method solves x^2 -69y^2=1
using the best rational approximations you can muster.
As you seem unable to actually use your own method,
perhaps it is not really your method at all.
arithmonic
wrote:
[cut sick andcowardly behavior]
Unidentified person, it is so easy for you to insult because you are
hiding your name and location. You are showing a real sick and
cowardly behavior.
The sci.math audience can see that you have no choice but to insult,
you and your friend have shown an unethical attitude and you should
cogitate on that.
***************************************************************************
********************
***************************************************************************
********************
> 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.
***************************************************************************
********************
***************************************************************************
********************
IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONIC
arithmonic
follows and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
Whatever...
There are very good news here, specially, for young people because
from now on, by means of simple arithmetic they will be able to learn
at secondary school --by means of the most simple arithmetic-- many
new simple higher-order algorithms, as well as all those well-known
cartesian-infinitesimal algorithms (i.e.: Halley's, Newton's,
Bernoulli's and Householder's) which have been considered as superb
achievements of the history of mathematics, however, one can see now
that all those "superb" achievements can be easily developed by means
of the most simple arithmetic.
Young student, be sure there is something very wrong with the whole
Cartesian-Infinitesimal scheme we have inherited.
Yours is the chance to find new ways on mathematics.
sttsc...@tesco.net
> On 25 jul, 16:22, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> Ask to Newton's , Halley's, etc. whatever you want to ask I have no
> intentions to answer
> any other question from you and your friend Grover Hughes.
Yes, because you cannot answer may questions.
Essentially you have no idea what you are talling about.
> If you think that you can make me upset, your are WRONG, so WRONG.
The capitalization alone suggets you are
disturbed in some way.
> 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?
I doubt they would obsess over something so trivial.
> 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.
How can you know this ?
Have you read every book published since
Babylonian times ?
Anyway, I'm beginning to doubt that the method
you claim to be yourrs is actually yours because
you don't know how to use it.
orang...@googlemail.com
> I would like to obtain this information.
take logs.
e.g. to find x= 5645746876^(1/3)
ln x = 1/3 ln 5645746876
x = e^(1/3 ln 5645746876)
works for any roots.
arithmonic
wrote:
[cut sick andcowardly behavior]
Unidentified person, it is so easy for you to insult because you are
hiding your name and location.
Indeed, I have never intended to be rude but you have shown a
psychopathic behavior.
***************************************************************************
I have never asserted in any posting from mine nor in my webpages, nor
in my book, nor in any paper that "The methods shown in my webpages
yield ALL THE BEST APPROXIMATIONS". There is nothing by far similar to
such assertion in my webpages and postings. That's why I posted again
my first posting in this and other threads. Of couse, these new simple
arithmetical methods yield best approximations and have high-order
convergence speed, and noone can deny such a STRIKING FACT.
***************************************************************************
The sci.math audience can read my webpages:
http://mipagina.cantv.net/arithmetic/rmdef.htm
there is nothing there by far similar to that you are trying to
falsely state in order cause confusion and prevent people from reading
my webpages. There were people in the past that devoted all his
efforts to cause the same confusion, and used all their means forming
packs and even sending me threatening private e-mails with virus,
worms, etc.
The sci.math audience can see that you have no choice but to insult,
you and your friend have shown an unethical attitude and you should
cogitate on that.
I have nothing more to add about the unethical attitude from you and
your friend.
Ask to Newton's , Halley's, etc. whatever you want to ask I have no
intentions to answer
any other question from you and your friend Grover Hughes.
If you think that you can make me upset, your are WRONG, so WRONG. I
do not look for any favors from neither any intitution nor any peer-
review journal. I really enjoy
what I am doing: TO TELL THE CRUDE TRUTH ABOUT THE WHOLE HISTORY OF
ROOT SOLVING.
I only regret that your so low self-esteem leads you to set such a
shameful example to young students. I regret that so much.
The simple high-order methods shown in my webpages have demolished
others in the past in the same way as they have done with both of you
(might be that some of you could be some of them, whatever...I do not
care).
So, from now on you will get the same message I gave to both of you
last time:
On 24 jul, 17:07, gwh <ghug...@cei.net> 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:
Grover Hughes negligently and unethically wrote: On 16 jul, 18:24, gwh
<ghug...@cei.net> wrote:
> 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.
******************************** ********************
******************************************************
> 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.
***************************************************************************
***************************************************************************
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.
sttsc...@tesco.net
> On 25 jul, 19:10, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> I have never asserted in any posting from mine nor in my webpages, nor
> in my book, nor in any paper that "The methods shown in my webpages
> yield ALL THE BEST APPROXIMATIONS".
You seem to be more adept at sophistry than maths
Can you prove that your method produces any
best approximations ? Not all, but any ?
When does your method produce best approximations
and when not?
Do you even understand what I am asking you ?
A simple proof will suffice.
I certainly won't be reading pages
of your mindless rantings which have no mathematical
significance whatsoever.
Why waste time with pointless verbiage when you
could provide a proof ?
sttsc...@tesco.net
> ***************************************************************************
> I have never asserted in any posting from mine nor in my webpages, nor
> in my book, nor in any paper that "The methods shown in my webpages
> yield ALL THE BEST APPROXIMATIONS". There is nothing by far similar to
> such assertion in my webpages and postings.
Not true see below:
"The point here is that a Rational Proccess which allow us
to trivially develop:
1.- Traditional and Generalized Continued Fractions"
University or The Math Forum.
Math Forum » Discussions » sci.math.* » sci.math
Topic: Wondering about Domingo's Rational Mean book
Replies: 32 Last Post: Jul 1, 2000 10:28 PM
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Domingo Gomez Morin
Posts: 215
Registered: 12/3/04
Re: Wondering about Domingo's Rational Mean book"
Posted: Jun 9, 2000 12:10 AM Plain Text Reply
In article <8hp1g8$47o$1...@barcode.tesco.net>,
"Iain Davidson" <Sttsc...@tesco.net> wrote:
>
> I don't think anyone would say that Farey
dissections are
less
fundamental
> than CFs, they are equivalent and both have
optimal
properties.
That´s right, all that has been said here is
that CFs
are just
a particular case of the rational process,
as can be easily seen by means of the following
example:
Given a set of two initial fractions:
[3/2, 4/3]
According to my definition and notation (see home
page),
the following very simple iteration algorithm:
(the symbol _ means subscript, and "Rm": Rational
Mean)
Rm[{3/2, 4/3},{2*3/2*2, 4/3}]=[7/5,10/7]
Rm[{7/5, 10/7},{2*7/5*2, 10/7}]=[17/12,24/17]
Rm[{17/12, 24/17},{2*17/12*2, 24/17}]=[41/29,58/41]
Rm[{41/29, 58/41},{2*41/29*2, 58/41}]=[99/70,140/99]
and so on....
is the most simple example of a Rational Process
for
aproximating
the square root of 2 (yielding sets of two fractions
whose
product
is always 2).
Thus, as everyone can see, this very simple rational
process
yields two column of values, the first one
(3/2, 7/5, 17/12, 41/29, 99/70,...) and
the second one
(4/3, 10/7, 24/17, 58/41, 140/99,...)
The first column (best approximations) corresponds
to
the simple CF representation of the square root of
2.
All this applies for all CFs, that is, not only for
simple
continued fractions and the particular case Mediant,
all CFs are just a column of values within a
rational process
of second order, however, there are other rational
processes
of higher order as can be seen in my home page.
Thus, noone will ever say there is any diference
between
traditional CFs and the Rational Process. You
mentioned above
"Farey dissections" (Mediant) and I´m forced
again to
remark
that the Mediant is just a special case of the
Rational Mean,
so the Rational Process embraces _ALL_ CFs.
The problem on finding all the best approximations
for
irrational of higher degrees is another matter,
in this way you said:
>
> However CFs have other useful feature like finding
quadratic
units,
> characterising rational and quadratic surds etc.
Again: the rational process embraces _all_ CFs.
>
> If your rational mean method is fundamental and
general then
it
should be
> capable
> of finding all solutions to the cubic analogue of
the Pell
Equation
>
> X^3 + kY^3 + (k^2)Z^3 - 3kXYZ = 1, k>1
>
> by finding best approximations to
cubt(k^2):cubrt(k):1
> as CFs do for sqrt(k):1 to solve X^2 -kY^2 = 1
I could tell you a very similar statement:
"If your CFs of second order is fundamental and
general then
it should
be
capable of finding all solutions to the cubic
analogue of the
Pell
Equation".
Although the point on best approximations is really
amusing
and useful,
I don´t feel that your particular definition
of
"fundamental and general" could be taken by far as
fundamental and general :-).
If someone feel compelled to ask me for a higher-
root method
which yields all the best approximations then I
could ask him
to do the same thing, that´s just fair.
The point here is that a Rational Proccess which
allow us
to trivially develop:
1.- Traditional and Generalized Continued Fractions
2.- Bernoulli´s method
3.- Newton´s method
4.- Halley´s method
5.- Power series expansions
5.- Many other new methods
6.- A new point of view on means definition
7.- A new definition of irrational numbers and
their
arithmetical
operations
is certainly a __general and fundamental__ concept,
moreover, when considering that we are talking about
a very simple __ARITHMETICAL__ method
(No derivatives, no decimals, no cartesian system)
which could have been easily implemented since
__ancient
times__,
unfortunatedly, "from all the evidences", ancient
mathematicians
were inexplicabily unaware of this general and
fundamental
concept.
The most general and fundamental news are that from
now on our
children
of scholar age will be able to easily handle, by
means of
simple
sums (simple arithmetic), all those "extremely
advanced"
methods (Newton´s and Halley´s) which
have been
sold to us
as exclusive, exquisite and sophisticated creations
of
the "divine" cartesian system.
That is the mean point here, and _I guess_ that was
one
of the reasons Proff. Kirby Urner asked for any
precedent
on the rational process at this newsgroup.
In the case he couldn´t get any answer from
sci.math on
this very
specific topic, I would suggest him to look at the
Historia-Matematica mailing list.
I know that all what I say could sound as harshly
talk (worst
Via internet), however, be sure this not directed
against
any individual but to the whole actual math-
scientific-system
and its terrible social consequences.
Indeed, I´m very grateful to all of you for
all your
comments, no matter
what they could be.
Finnally I must publicy say that I´m greatly
impressed,
indeed,
by the wonderful and amusing Kirby´s web-
pages at:
http://www.inetarena.com/~pdx4d/ocn/numeracy0.html
This means there is still people who really care for
our young people.
Greetings,
Domingo Gomez Morin
Date Subject Author
5/30/00 Wondering about Domingo's Rational Mean book
Kirby Urner
5/30/00 Re: Wondering about Domingo's Rational Mean book
Kirby Urner
5/30/00 Re: Wondering about Domingo's Rational Mean book
Iain Davidson
5/31/00 Re: Wondering about Domingo's Rational Mean book
Kirby Urner
5/31/00 Re: Wondering about Domingo's Rational Mean book
Iain Davidson
6/1/00 Re: Wondering about Domingo's Rational Mean book
Kirby Urner
6/7/00 "Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/8/00 Re: Wondering about Domingo's Rational Mean book"
Iain Davidson
6/9/00 Re: Wondering about Domingo's Rational Mean book"
Domingo Gomez Morin
6/10/00 Re: Wondering about Domingo's Rational Mean
book"
Iain Davidson
6/12/00 Re: Wondering about Domingo's Rational Mean book
Domingo Gomez Morin
6/12/00 Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/13/00 Re: Wondering about Domingo's Rational Mean
book"
Iain Davidson
6/14/00 Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/14/00 Re: Wondering about Domingo's Rational Mean
book"
Iain Davidson
6/14/00 Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/14/00 Re: Wondering about Domingo's Rational Mean
book"
Huaiyu Zhu
6/17/00 Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/16/00 Re: Wondering about Domingo's Rational Mean
book"
Iain Davidson
6/17/00 Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/18/00 Re: Wondering about Domingo's Rational Mean
book"
david_...@my-deja.com
6/19/00 Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
6/20/00 Is this new, rational means?
Milo Gardner
6/21/00 Re: Is this new, rational means?
Domingo Gomez Morin
6/22/00 inverse golden proportion
Milo Gardner
6/22/00 Re: inverse golden proportion
Domingo Gomez Morin
6/23/00 Archimedes' finite numeration system, and
calculus
Milo Gardner
6/29/00 Wondering about Domingo´s rational mean book
Domingo Gomez Morin
6/30/00 Archimedes used Egyptian finite arithmetic to
solve
4A/3 and n/pq conversion
Milo Gardner
7/1/00 Re: Archimedes used Egyptian finite arithmetic to
solve 4A/3 and n/pq conversion
Domingo Gomez Morin
7/1/00 Re: Is this new, rational means?
Domingo Gomez Morin
5/31/00 Re: Wondering about Domingo's Rational Mean book
Kirby Urner
6/7/00 "Re: Wondering about Domingo's Rational Mean
book"
Domingo Gomez Morin
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arithmonic
wrote:
[cut sick and cowardly behavior hiding his name]
Unidentified person, it is so easy for you to insult because you are
hiding your name.
Indeed, I have never intended to be rude but you have shown a
psychopathic behavior.
The requisite for any root-solving algorithm to be considered as that,
is NOT about if it yields best approximations, is about its true
convergence to the root, there is plenty info on convergence criteria.
If the algorithms yield best approximations then that's great¡, that's
fine, but best approximations are not the requisite for asserting
that a method converge. indeed, you are certainly showing a
psychopathic behavior in the same way as others did in the past (I am
not quite sure if you are one of them hiding your name).
Of course, the methods shown in my webpages embrace --among many other
new algorithms-- the traditional continued fractions of second degree,
Newton's method, halley's method, Householder's method etc. and
certainly yield best approximations.
That's true and anyone can see that in my webpages.
I even understand your feelings, probably you have read some books on
numerical methods (based on infinitesimals, fluxions, etc.) and the
history of root-solving, and now you realize that halley's,
Householder's methods for approximating roots as well as many other
new iterating functions could have been TRIVIALLY developed by means
of the MOST SIMPLE ARITHMETIC.
That is bitter blow for you and some others. I am sorry for you but
you have to
swallow it.
But...
***************************************************************************
I have never asserted in any posting from mine nor in my webpages,
nor
in my book, nor in any paper that:
"The methods shown in my webpages yield ALL THE BEST
APPROXIMATIONS".
There is nothing by far similar to such assertion in my webpages and
postings. That's why I posted again my first posting in this and other
threads. Of couse, these new simple arithmetical methods yield best
approximations and have high-order convergence speed, and noone can
deny such a STRIKING FACT.
You just need to show to the sci.math audience just a single phrase
from mine stating:
"The methods shown in my webpages yield ALL THE BEST
APPROXIMATIONS".
But you cannot because that is another lie from yours pretending to
cause confusion as some others tried in the past and had no success.
***************************************************************************
The sci.math audience can read my webpages:
http://mipagina.cantv.net/arithmetic/rmdef.htm
there is nothing there by far similar to that you are trying to
falsely state, that is: "The methods shown in my webpages yield ALL
THE BEST APPROXIMATIONS".
The sci.math audience can see that you have no choice but to insult,
you and your friend have shown an unethical attitude and you should
cogitate on that.
I have nothing more to add about the unethical attitude from you and
your friend.
Ask to Newton's , Halley's, etc. whatever you want to ask I have no
intentions to answer
any other question from you and your friend Grover Hughes.
If you think that you can make me upset, your are WRONG, so WRONG. I
do not look for any favors from neither any intitution nor any peer-
review journal. I really enjoy
what I am doing: TO TELL THE CRUDE TRUTH ABOUT THE WHOLE HISTORY OF
ROOT SOLVING.
I only regret that your so low self-esteem leads you to set such a
shameful example to young students. I regret that so much.
The simple high-order methods shown in my webpages have demolished
others in the past in the same way as they have done with both of you
(might be that some of you could be some of them, whatever...I do not
care).
I even understand your feelings, probably you have read some books on
numerical methods and now realize that halley's, Householder's and
many other new iterating functions could have been developed by means
of the MOST SIMPLE ARITHMETIC.
That is bitter blow for you and some others, I am sorry for that but
you have to
swallow it.
>From now on you will get the same message I gave to both of you
arithmonic
wrote:
[cut ]
Unidentified person, it is so easy for you to insult because you are
hiding your name.
Indeed, I have never intended to be rude but you have shown a
psychopathic behavior.
The requisite for any root-solving algorithm to be considered as that,
is NOT about if it yields best approximations, is about its true
convergence to the root, there is plenty info on convergence criteria.
If the algorithms yield best approximations then that's great¡, that's
fine, but best approximations are not the requisite for asserting
that a method converge. indeed, you are certainly showing a
psychopathic behavior in the same way as others did in the past (I am
not quite sure if you are one of them hiding your name).
Of course, the methods shown in my webpages embrace --among many other
new algorithms-- the traditional continued fractions of second degree,
Newton's method, halley's method, Householder's method etc. and
certainly yield best approximations.
That's true and anyone can see that in my webpages.
I even understand your feelings, probably you have read some books on
numerical methods (based on infinitesimals, fluxions, etc.) and the
history of root-solving, and now you realize that halley's,
Householder's methods for approximating roots as well as many other
new iterating functions could have been TRIVIALLY developed by means
of the MOST SIMPLE ARITHMETIC.
That is bitter blow for you and some others. I am sorry for you but
you have to
swallow it.
But...
***************************************************************************
I have never asserted in any posting from mine nor in my webpages,
nor
in my book, nor in any paper that:
"The methods shown in my webpages yield ALL THE BEST
APPROXIMATIONS".
There is nothing by far similar to such assertion in my webpages and
postings. That's why I posted again my first posting in this and other
threads. Of couse, these new simple arithmetical methods yield best
approximations and have high-order convergence speed, and noone can
deny such a STRIKING FACT.
You just need to show to the sci.math audience just a single phrase
from mine stating:
"The methods shown in my webpages yield ALL THE BEST
APPROXIMATIONS".
But you cannot because that is another lie from yours pretending to
cause confusion as some others tried in the past and had no success.
***************************************************************************
The sci.math audience can read my webpages:
http://mipagina.cantv.net/arithmetic/rmdef.htm
there is nothing there by far similar to that you are trying to
falsely state, that is: "The methods shown in my webpages yield ALL
THE BEST APPROXIMATIONS".
The sci.math audience can see that you have no choice but to insult,
you and your friend have shown an unethical attitude and you should
cogitate on that.
I have nothing more to add about the unethical attitude from you and
your friend.
Ask to Newton's , Halley's, etc. whatever you want to ask I have no
intentions to answer
any other question from you and your friend Grover Hughes.
If you think that you can make me upset, your are WRONG, so WRONG. I
do not look for any favors from neither any intitution nor any peer-
review journal. I really enjoy
what I am doing: TO TELL THE CRUDE TRUTH ABOUT THE WHOLE HISTORY OF
ROOT SOLVING.
I only regret that your so low self-esteem leads you to set such a
shameful example to young students. I regret that so much.
The simple high-order methods shown in my webpages have demolished
others in the past in the same way as they have done with both of you
(might be that some of you could be some of them, whatever...I do not
care).
I even understand your feelings, probably you have read some books on
numerical methods and now realize that halley's, Householder's and
many other new iterating functions could have been developed by means
of the MOST SIMPLE ARITHMETIC.
That is bitter blow for you and some others, I am sorry for that but
you have to
swallow it.
>From now on you will get the same message I gave to both of you
arithmonic
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.
sttsc...@tesco.net
> On 26 jul, 04:37, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
> [cut sick and cowardly behavior hiding his name]
You are truly a lamentable fool and liar.
You claim in the posting that I cite that
the rational mean is the basis for all continued fractions
and generalized continued fractions.
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.
sttsc...@tesco.net
> [everything cut - my head is starting to spin!]
>
> Here is an OT quote which, if followed, might help the readability of
> this thread:
>
> "Vigorous writing is concise. A sentence should contain no unnecessary
> words, a paragraph no unnecessary sentences, for the same reason that
> a drawing should have no unnecessary lines and a machine no
> unnecessary parts. This requires not that the writer make all his
> sentences short, or that he avoid all detail and treat his subjects
> only in outline, but that every word tell."
Sorry, I thought I was being relatively concise under the
circumstances. What don't you understand ?
The proliferation of arguments is a classic Dumbingo
tactic to cloud the issue.
arithmonic
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]
>
> 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:
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
arithmonic
> On Jul 26, 12:47 pm, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> failed to make any new points - and attempting to do so
> diplomatically. Doubtless it is a futile exercise - anyone with an
> overfondness for capital letters is unlikely to value good writing.
> Your points have been easy to understand - though I am not in a
> position to judge the extent to which his methods differ from those
> already appearing in the literature. Frankly, I don't care very much
> since I am not exactly pining for methods for extracting roots - a
> computer algebra system can give me hundreds of digits of precision in
> small fractions of a second, which is way more than I'll ever need.
> The topic is probably interesting and could make a good article for
> say the MAA Monthly, but it is not exactly cutting edge.- Ocultar texto de la cita -
>
> - Mostrar texto de la cita -
Another anonymous, I think that anonymous are proliferating in this
thread, I wonder why.
What a fun.
>I was responding to a prolix message from arithmonic in which he
> failed to make any new points
YOU ARE WRONG, I DIDN'T FAILED, I AM NOT INTERESTED IN RISING ANY
OTHER NEW POINT FOR
SUCH AN ANONYMOUS PSYCHOPATH like this: sttscitr...@tesco.net.
So I am only replying him by copying and pasting with just some
additional words in each new posting.
You also said: "I don't care very much since I am not exactly ...."
THEN, IF YOU DO NOT CARE: What are you doing here?
Go elsewhere, find a girl, drive a car, whatever you could ever really
care.
> The topic is probably interesting and could make a good article for
> say the MAA Monthly, but it is not exactly cutting edge.
All these new methods are not looking for any favor neither from
intitutions nor from any journal in exchange for not including my
critics on the whole history of root-solving. My critics will
always be along with these methods, and that will make nothing good
for any peer-review journal.
I will not send these methods to any re-known peer-review journal.
Math-historians have a MORAL OBLIGATION: TO INCLUDE THESE METHODS IN
THEIR PAPERS.
If they are not willing to do that, I don't care. The transcendence of
these methods do not depend on neither any journals, nor normal
persons, nor myself, nor on any anonymous postings.
These methods will inebitably find their way all through young minds --
not among anonymous parrot-fashion psychopathic cowards, of course--.
> computer algebra system can give me hundreds of digits of precision in
> small fractions of a second, which is way more than I'll ever need.
Well, let us wish you a life FULL OF JOY to you and your software,
and your ANONYMOUS BEHAVIOR which is something far WORSE than any typo
or philological error that someone could ever commit. Just, two cents
to you.
Few people feel some respect for ANONYMOUS POSTINGS.
SO SORRY, IF YOU DON'T LIKE CAPITAL LETTERS.
ing. Domingo Gomez Morin
Structural Engineer
Caracas
venezuela
arithmonic
Summarizing, a bunch of parrot-fashion psychopaths who enjoy anonymity
because of their cowardice and incapacity to prevent people from
learning these new methods :
1.- Failed to present any precedents on the new simple methods based
on the Rational Mean
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
2.- Failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
4.- Failed to try to discredit the new extremely simple high-order
arithmetical algorithms by stating that they do not produce best
approximations (which is of course another lie that anyone can confirm
by reading my wepages), because they are not acquainted with the fact
that any root-solving algorithm only need to hold true convergence
towards the root value (according to the standard convergence
criteria), so the issue on best approximations is by no means a
requisite for being considered as a trully good algorithm. Their
ignorance on mathematics does not matter, at all, but their
psychopathic behavior and stupidity is really disgusting.
3.- Showed a shameful unethical and psychopathic behavior and huge
cheeks, and of course
a cowardly tendency to anonymity.
4.- Failed their attempts to try to divert the issue on root-solving
to the issue on philology and gramatical use of the phrase :
"GENERALIZED CONTINUED FRACTION".
Considering their anonymous parrot-fashion psychopath behavior I am
now so worried that they could actually be math teachers, I hope they
don't, indeed, but might it be.
Actually, in so many schools we have witnessed many irrational and
violent actions of young students when reacting against their
teachers.
Now that I think that, I am so worried about these parrot-fashion
psychopaths
So...to the point on the essence of all this thread:
As said in the first posting of this thread, I face and maintain what
follows and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
Whatever...
There are very good news here, specially, for young people because
from now on, by means of simple arithmetic they will be able to learn
at secondary school --by means of the most simple arithmetic-- many
new simple higher-order algorithms, as well as all those well-known
cartesian-infinitesimal algorithms (i.e.: Halley's, Newton's,
Bernoulli's and Householder's) which have been considered as superb
achievements of the history of mathematics, however, one can see now
that all those "superb" achievements can be easily developed by means
of the most simple arithmetic.
Young student, be sure there is something very wrong with the whole
Cartesian-Infinitesimal scheme we have inherited.
Yours is the chance to find new ways on mathematics.
Ing. Domingo Gomez Morin
Structural Engineer
Caracas Venezuela
sttsc...@tesco.net
I wonder if Gottfried Helms still thinks your contribution to
mathematical knowledge is still quite so fantastic.
At least he can have no doubts that you are
teetering on the verge of insanity.
> 1.- Failed to present any precedents on the new simple > methods based on the Rational
Your method is facile, who but a retard would wriite it down
for posterity ?
>
> 2.- Failed to present any posting from mine stating: "My methods > always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
> that but failed.
Your post that I cited clearly confirms that you
claim to produce generalized continued fractions
from the "rational mean". It's not a continued fraction
unless it can produce preferably all but at least some
best rational simultaneous approximation.
Presumably, your generalized continued fractions can produce at least
one best rational simultaneous
approximation. If so produce a BRSA to
cubt(69*69), cubrt(69).
You won't be able to because you have no idea
whatsoever what you are taling about.
Childish whining deleted.
arithmonic
wrote:
> 1.- Failed to present any precedents on the new simple > methods
based on the Rational
> Your method is facile, who but a retard would wriite it down
> for posterity ?
I was sure that you was close to begin to cowardly insult many other
people (who are not inhabiting this newgroup) as everybody can meet at
the links included in the webpage :
http://mipagina.cantv.net/arithmetic
Generalized Continued Fractions is another issue, and is clearly
explained at the webpage:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
The issue on the way continued fractions have been treated all through
the history is precisely the essence of critics of that GCF webpage.
The most relevant aspect of these very particular Generalized
Continued Fractions is that they allow to find periodic
representations of irrational numbers of higher degree. And such GCF
were devised exclusively by agency of the Rational Mean, that's what
all my postings and webpage state.
Neither one single posting from mine, nor the GCF webpage state that
such generalization of continued fractions yield all the best
approximations for all the irrational numbers. On the contrary, the
webpage only talks about a new periodic representation of irrational
numbers of degree higher than 2, and bring numerical samples which
clearly show that, for instance, in the case of the cube root some
convergents are best approximations while others not. And your
psychopathic and coward behavior cannot hide such numerical samples.
So you want me to name those fractions the way you want?
You are wrong, a real imbecile like you that feel yourself so brave
by hiding your name behind a computer and insulting people, cannot
bring anything of interest to me. Cowards have nothing to bring,
indeed.
Why do you hide your name? What are you afraid of?
Neither you, nor any other person HAVE INVENTED any single
"Generalized Continued Fraction" bringing ALL THE BEST APPROXIMATIONS
as well as the periodic representation of irrational numbers of degree
higher than 2.
So, the only thing that make you think that you can make your stupid
comments and insult people the way you do, as well as to force others
to name something (that you are absolutely unable to invent) the way
you think it should be, is only your psychopathic behavior.
The word "Continued" does not mean anything related to best
approximations,
that's why mathematicians had to create the phrase "Simple Continued
Fractions" so it can be differentiated from those who not necesarily
yield all the best approximations. Of course, that's so hard to
understand for you. You even pretend to ignore that such words (even
the word: "Simple") has been an issue for debate among many people.
You are a complete parrot-fashion 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
issues about GCF.
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.
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
arithmonic
anonymity
because of their cowardice and incapacity to prevent people from
learning these new methods :
1.- Failed to present any precedents on the new simple methods based
on the Rational Mean
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
2.- Failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
arithmonic
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake. You have finally shown the true reason for your
insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, you are far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find
of some interest those methods, nor about a me (on the contrary, I did
not consider such methods as "my methods" even when sometimes for the
sake of brevity I am forced to use such words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
Indeed, I think this guy <sttscitr...@tesco.net> should be
investigated, because if he acts
like a math teacher in any school then we have a serious problem.
sttsc...@tesco.net
> On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
> The issue on the way continued fractions have been treated all through
> the history is precisely the essence of critics of that GCF webpage.
> The most relevant aspect of these very particular Generalized
> Continued Fractions is that they allow to find periodic
> representations of irrational numbers of higher degree. And such GCF
> were devised exclusively by agency of the Rational Mean, that's what
> all my postings and webpage state.
Utter drivel.
Let's see you derive the Jacobi-Perron type of
generalized continued fraction from the rational mean.
sttsc...@tesco.net
> approximations,
> that's why mathematicians had to create the phrase "Simple Continued
> Fractions" so it can be differentiated from those who not necesarily
> yield all the best approximations. Of course, that's so hard to
> understand for you. You even pretend to ignore that such words (even
> the word: "Simple") has been an issue for debate among many people.
Dumbingo, the only thing around here that is simple
is you. You prove this fact time and time again with your inane
ramblings.
arithmonic
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
Poor litle man, for God sake. You have finally shown the true reason
for your insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, you are far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find
of some interest those methods, nor about a me (on the contrary, I
did
not consider such methods as "my methods" even when sometimes for the
sake of brevity I am forced to use such words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
Indeed, I think this guy <sttscitr...@tesco.net> should be
investigated, because if he acts
like a math teacher in any school then we have a serious problem.
Come on show up your name and be so brave by continuing your insults
against these people: http://mipagina.cantv.net/arithmetic
Come on you so litle envious coward.
I was sure that your despair could drive you to cowardly insult many
arithmonic
wrote:
[CUT just insults against people who do not inhabit this newsgroup]
This litle envious man: <sttscitr...@tesco.net> cannot put his
signature
to any single insult from him.
Summarizing, a parrot-fashion psychopath who enjoy
anonymity because of their cowardice and incapacity to prevent people
from
learning these new methods :
1.- Failed to present any precedents on the new simple methods based
on the Rational Mean
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
2.- Failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
4.- Failed to try to discredit the new extremely simple high-order
arithmetical algorithms by stating that they do not produce best
approximations (which is of course another lie that anyone can
confirm by reading my wepages).
The litle envious man are not acquainted with the fact that any root-
solving algorithm only need to hold true convergence
towards the root-value (according to the standard convergence
criteria), so the issue on best approximations is by no means a
requisite for being considered as a trully good algorithm. Their
ignorance on mathematics does not matter, at all, but their
psychopathic behavior and stupidity is really disgusting.
3.- Showed a shameful unethical and psychopathic behavior and huge
cheeks, and of course a cowardly tendency to anonymity. So this
litle
envious man cannot put his signature to his rash comments.
4.- Failed their attempts to try to divert the issue on root-solving
to the issue on philology and gramatical use of the phrase :
"GENERALIZED CONTINUED FRACTION".
Considering their anonymous parrot-fashion psychopath behavior I am
now so worried that they could actually be math teachers, I hope
they don't, indeed, but might it be.
So...to the point on the essence of all this thread:
As said in the first posting of this thread, I face and maintain what
follows and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
arithmonic
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake, poor litle envious man. You have finally shown the true
reason for your insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, you are far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find of some interest those methods, nor about
a me (on the contrary, I did not consider such methods as "my methods"
even when sometimes for the sake of brevity I am forced to use such
words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
Indeed, I think this guy <sttscitr...@tesco.net> should be
investigated, because if he acts
like a math teacher in any school then we have a serious problem.
You have now decided to insult other people who have kindly devoted
some of their unvaluable time to analyze these new methods and to try
to bring something new from them, and that is something that I cannot
tolerate.
They have published some of their ideas on some of these methods and I
am sure that most of them do not agree with many critics or comments
from mine (and I do not want them to do so), but they have an open
mind and don't think about themselves as owners of Truth.
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
Come on show up your name, your signature does not support any single
insult and false statement you have made. Come on, be a man.
Ing. Domingo Gomez
Structural Engineer
Caracas
Venezuela
sttsc...@tesco.net
You GCF stuff is complete rubbish.
You claim that you can express the root of
a monic polynomial x^n +a_n-1x^(n-1) + +a_0=0
in terms of its coeficients (integer, rational, complex
you do not say), but an equation of this kind can
have all complex roots with rational coefficients.
How can a complex number be expressed as a
ratio rational numbers ?
What is the GCF expansion of the largest root of x^2 +1 ?
Where are the details of Ronan Larkin's work ?
Are you a mathematician or an engineer ?
arithmonic
wrote:> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake, poor litle envious man. You have finally shown the true
reason for your insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, you are far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find of some interest those methods, nor
about
a me (on the contrary, I did not consider such methods as "my
methods"
even when sometimes for the sake of brevity I am forced to use such
words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
Indeed, I think this guy <sttscitr...@tesco.net> should be
investigated, because if he acts
like a math teacher in any school then we have a serious problem.
You have now decided to insult other people who have kindly devoted
some of their unvaluable time to analyze these new methods and to try
to bring something new from them, and that is something that I cannot
tolerate.
They have published some of their ideas on some of these methods and
I
am sure that most of them do not agree with many critics or comments
from mine (and I do not want them to do so), but they have an open
mind and don't think about themselves as owners of Truth.
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
Come on show up your name, your signature does not support any single
insult and false statement you have made. Come on, be a man.
You are just an ignorant who does not know that the general Rational
Mean concept trivially leads the way to the well-known Daniel
Bernoulli's method and at the same time allowed to devise these new
GCF (which basically are the well-known Bernoulli's method as stated
in my book and webpage, so it is clear that I could never intend to
say that such GCF produce all the best approximations for any
irrational number).
You are just a litle envious man who ignores the required steps to
apply the well-known Daniel Bernoulli's method to complex roots.
You are clearly unable to recognize that such GCF are basically Daniel
Bernoulli's method.
You are clearly unable to realize that I don't care about the
importance of such very particular GCF expression shown in my
webpages, because there are many others, and that is not the true
issue of my work. Actually, the GCF expression shown in the webpage:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
are just a bit sample of an uncountable number of similar single
continued expressions that you can find to express irrational
numbers.
You are clearly unable to realize that I believe it can be found a
missing mathematics, a true natural mathematics that does not require,
at all, any BIZARRE Imaginary Number Concept, notice that I say
bizarre even when some people have found practical applications for
them. I think that a true natural science of mathematics should not be
just a bunch of bizarre tricks and patches whic have been forced to
match some particular needs.
Consequently, you are unable to realize that I do not care about the
bizarre imaginary numbers concept (even when they are widely applied
in engineering).
I think that Imaginary numbers are not part of a true natural science
but just TRICKS AND PATCHES.
I am sure there is a missing mathematics based on Number itself, which
is not composed neither of just TRICKS-&-PATCHES (like modern
mathematics), nor of TRIAL-&-ERRORS METHODS like those you pretended
to pass as precedents of these new ways.
All that is explained in my webpages and book, of course, your parrot-
fashion mind and your tendency to insult people who do not inhabit
this newsgroup will not allow you to understand a single bit of all
what I am talking about. That's it.
sttsc...@tesco.net
> wrote:
> On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
> You are just an ignorant
Well, you should be able to explain to the ignorant how this works.
> You are clearly unable to realize that I believe it can be found a
> missing mathematics, a true natural mathematics that does not require,
> at all, any BIZARRE Imaginary Number Concept, notice that I say
> bizarre even when some people have found practical applications for
> them. I think that a true natural science of mathematics should not be
> just a bunch of bizarre tricks and patches whic have been forced to
> match some particular needs.
Really, you are even nuttier than I first thought.
Some achievement on your part.
> Consequently, you are unable to realize that I do not care about the
> bizarre imaginary numbers concept (even when they are widely applied
> in engineering).
So what are the roots of x^2 +1 = 0 or x^4 +1 =0?
> I think that Imaginary numbers are not part of a true natural science
> but just TRICKS AND PATCHES.
Really ?
Why that ?
arithmonic
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake, poor litle envious man. You have finally shown the true
reason for your insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, your stupidity is far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find of some interest those methods, nor
about
a me (on the contrary, I did not consider such methods as "my
methods"
even when sometimes for the sake of brevity I am forced to use such
words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
http://mipagina.cantv.net/arithmetic
That's why the central idea of all my postings is just about the
new general Rational Mean concept and the new hig-order arithmetical
root-solving algorithms (not about those samples on GCF) that have no
precedents, at all, as your stupidity have finally allow you to
realize.
You are clearly unable to realize that I believe it can be found a
missing mathematics, a true natural mathematics that does not
require,
at all, any BIZARRE Imaginary Number Concept, notice that I say
bizarre even when some people have found practical applications for
them. I think that a true natural science of mathematics should not
be
just a bunch of bizarre tricks and patches whic have been forced to
match some particular needs.
Consequently, you are unable to realize that I do not care about the
bizarre imaginary numbers concept (even when they are widely applied
in engineering).
I think that Imaginary numbers are not part of a true natural science
but just TRICKS AND PATCHES.
sttsc...@tesco.net
> On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
> Well, your stupidity is far beyond any help, indeed.
In that case why are you writing screeds in reply?
You have nothing worthwhile to say and you cannot
answer any of my questions.
Your own words have demonstrated that you
are ignorant and mentally unstable, which
was my intention.
arithmonic
wrote:
> You GCF stuff is complete rubbish.
You got to this point with nothing more than to insult because you
ignored that one of the most important characteristics of the very
particular sample on GCF
(I say "very particular" because there is an uncountable number of GCF
which differs from that)
shown in the webpage: http://mipagina.cantv.net/arithmetic/gencontfrac.htm
IS THAT SUCH GCF IS JUST A REPRESENTATION OF DANIEL BERNOULLI'S METHOD
FOR ROOT-SOLVING, which at the same time is es PERIODIC CONTINUED-
FRACTION REPRESENTATION of irrational numbers of degree higher than
2. With the particularity that all this concept was TRIVIALLY devised
by agency of the Rational Mean processes.
Your stupidity, envy, cowardice and psychopathic behavior drived you
to fall in such a rat-trap which has been specially settled for
overbearing ignorants like you. So anything you want to tell about
such GCF is automatically applied to Daniel Bernoulli's method.
Now, you want me to explain to you how the Lineal Homogeneous
Recurrence Relations of Daniel Bernoulli's method works with complex
numbers. WRONG, take a book by yourself and learn that method, and
slow down your overbearing ignorance.
I do not bring any cent for the bizarre Trick-&.Patch called:
Imaginary Numbers.
You are far beyond any help, indeed.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake, poor litle envious man. You have finally shown the true
reason for your insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, your stupidity is far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find of some interest those methods, nor
about
a me (on the contrary, I did not consider such methods as "my
methods"
even when sometimes for the sake of brevity I am forced to use such
words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
arithmonic
1.- You failed to present any precedents on the new simple methods
based
on the Rational Mean
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
2.- You failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
4.- You failed to try to discredit the new extremely simple high-
order
arithmetical algorithms by stating that they do not produce best
approximations (which is of course another lie that anyone can
confirm by reading my wepages).
The litle envious man are not acquainted with the fact that any
root-
solving algorithm only need to hold true convergence
towards the root-value (according to the standard convergence
criteria), so the issue on best approximations is by no means a
requisite for being considered as a trully good algorithm. Their
ignorance on mathematics does not matter, at all, but their
psychopathic behavior and stupidity is really disgusting.
3.- You showed a shameful unethical and psychopathic behavior and
huge
cheeks, and of course a cowardly tendency to anonymity. So this
litle
envious man cannot put his signature to his rash comments.
4.- You failed their attempts to try to divert the issue on root-
solving
to the issue on philology and gramatical use of the phrase :
"GENERALIZED CONTINUED FRACTION". And you were not acquainted with the
fact that one of the most important characteristics of the very
particular sample on GCF shown in the webpage:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
IS THAT SUCH GCF IS JUST A REPRESENTATION OF DANIEL BERNOULLI'S
METHOD
FOR ROOT-SOLVING, which at the same time is es PERIODIC CONTINUED-
FRACTION REPRESENTATION of irrational numbers of degree higher than
2. With the particularity that all this concept was TRIVIALLY devised
by agency of the Rational Mean processes.
Your stupidity, envy, cowardice and psychopathic behavior drived you
to fall in such a rat-trap which has been specially settled for
overbearing ignorants like you. So anything you want to tell about
such GCF is automatically applied to Daniel Bernoulli's method.
Now, you want me to explain to you how the Lineal Homogeneous
Recurrence Relations of Daniel Bernoulli's method works with complex
numbers. WRONG, take a book by yourself and learn that method, and
slow down your overbearing ignorance.
Based on the above considerations, I face and maintain what follows
and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
sttsc...@tesco.net
> You are just a litle envious man who ignores the required steps to
> apply the well-known Daniel Bernoulli's method to complex roots.
You are simply contradicting yourself.
If you think complex numbers are "tricks amd patches"
(whatever that might mean) ,are you saying that
complex numbers don't exist or their use should be avoided
or what ?
If x^4 +2 = 0 and the roots are complex and Bernoulli's
method gives complex numbers as roots (what else ?)
your GCF can't be equivalent to Bernoulli's method
because your GCFs produce only
rational numbers. Your GCF involves only ratios of the coefficients
1,2.
Please try and give a straight answer to this question
instead of evading the issue all the time.
If the answer is in your book you can reproduce it here.
Mindless repetition of the same mantra is not rational
discourse. You are the one making the claims about
your GCF, it is not for others to puzzle about what you
may or may not mean. If you have a cogent explanation,
please give one.
arithmonic
> You GCF stuff is complete rubbish.
You got to this point with nothing more than to insult because you
ignored that one of the most important characteristics of the very
particular sample on GCF
(I say "very particular" because there is an uncountable number of
GCF
which differs from that)
shown in the webpage: http://mipagina.cantv.net/arithmetic/gencontfrac.htm
IS THAT SUCH GCF IS JUST A REPRESENTATION OF DANIEL BERNOULLI'S
METHOD
FOR ROOT-SOLVING, which at the same time is es PERIODIC CONTINUED-
FRACTION REPRESENTATION of irrational numbers of degree higher than
2. With the particularity that all this concept was TRIVIALLY devised
by agency of the Rational Mean processes.
Your stupidity, envy, cowardice and psychopathic behavior drived you
to fall in such a rat-trap which has been specially settled for
overbearing ignorants like you. So anything you want to tell about
such GCF is automatically applied to Daniel Bernoulli's method.
Now, you want me to explain to you how the Lineal Homogeneous
Recurrence Relations of Daniel Bernoulli's method works with complex
numbers. WRONG, take a book by yourself and learn that method, and
slow down your overbearing ignorance.
I do not bring any cent for the bizarre Trick-&.Patch called:
Imaginary Numbers.
You are far beyond any help, indeed.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake, poor litle envious man. You have finally shown the true
reason for your insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, your stupidity is far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find of some interest those methods, nor
about
a me (on the contrary, I did not consider such methods as "my
methods"
even when sometimes for the sake of brevity I am forced to use such
words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
http://mipagina.cantv.net/arithmetic
You are just a litle envious man who ignores the required steps to
apply the well-known Daniel Bernoulli's method to complex roots.
arithmonic
1.- You failed to present any precedents on the new simple methods
based
on the Rational Mean
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
2.- You failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
4.- You failed to try to discredit the new extremely simple high-
order
arithmetical algorithms by stating that they do not produce best
approximations (which is of course another lie that anyone can
confirm by reading my wepages).
The litle envious man are not acquainted with the fact that any
root-
solving algorithm only need to hold true convergence
towards the root-value (according to the standard convergence
criteria), so the issue on best approximations is by no means a
requisite for being considered as a trully good algorithm. Their
ignorance on mathematics does not matter, at all, but their
psychopathic behavior and stupidity is really disgusting.
3.- You showed a shameful unethical and psychopathic behavior and
huge
cheeks, and of course a cowardly tendency to anonymity. So this
litle
envious man cannot put his signature to his rash comments.
4.- You failed their attempts to try to divert the issue on root-
solving
to the issue on philology and gramatical use of the phrase :
"GENERALIZED CONTINUED FRACTION". And you were not acquainted with
the
fact that one of the most important characteristics of the very
particular sample on GCF shown in the webpage:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
IS THAT SUCH GCF IS JUST A REPRESENTATION OF DANIEL BERNOULLI'S
METHOD
FOR ROOT-SOLVING, which at the same time is es PERIODIC CONTINUED-
FRACTION REPRESENTATION of irrational numbers of degree higher than
2. With the particularity that all this concept was TRIVIALLY devised
by agency of the Rational Mean processes.
Your stupidity, envy, cowardice and psychopathic behavior drived you
to fall in such a rat-trap which has been specially settled for
overbearing ignorants like you. So anything you want to tell about
such GCF is automatically applied to Daniel Bernoulli's method.
Now, you want me to explain to you how the Lineal Homogeneous
Recurrence Relations of Daniel Bernoulli's method works with complex
numbers. WRONG, take a book by yourself and learn that method, and
slow down your overbearing ignorance.
Based on the above considerations, I face and maintain what follows
and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
sttsc...@tesco.net
> On 27 jul, 09:54, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
Again you are not giving a straight answer to a straight question.
Keep to the point.
I'll keep it simple.
What you are saying about complex
numbers is not clear
How would you solve x^2 +1 =0
What are it's roots ?
Are you saying
a) x^2+1 = 0 has no roots
b) x^2 +1 = 0 has rational roots
c) Something else ?
d) if c) then what precisley ?
arithmonic
The day you find some precedents in any text from past time on all the
simple hig-order arithmetical methods shown in my webpages (as you
falsely promised to the sci.math audience, and failed to do so),only
then, I will be willing to answer any other question.
arithmonic
1.- You failed to present any precedents on the new simple methods
based
on the Rational Mean
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
2.- You failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
4.- You failed to try to discredit the new extremely simple high-
order
arithmetical algorithms by stating that they do not produce best
approximations (which is of course another lie that anyone can
confirm by reading my wepages).
The litle envious man are not acquainted with the fact that any
root-
solving algorithm only need to hold true convergence
towards the root-value (according to the standard convergence
criteria), so the issue on best approximations is by no means a
requisite for being considered as a trully good algorithm. Their
ignorance on mathematics does not matter, at all, but their
psychopathic behavior and stupidity is really disgusting.
3.- You showed a shameful unethical and psychopathic behavior and
huge
cheeks, and of course a cowardly tendency to anonymity. So this
litle
envious man cannot put his signature to his rash comments.
4.- You failed their attempts to try to divert the issue on root-
solving
to the issue on philology and gramatical use of the phrase :
"GENERALIZED CONTINUED FRACTION". And you were not acquainted with
the
fact that one of the most important characteristics of the very
particular sample on GCF shown in the webpage:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
IS THAT SUCH GCF IS JUST A REPRESENTATION OF DANIEL BERNOULLI'S
METHOD
FOR ROOT-SOLVING, which at the same time is es PERIODIC CONTINUED-
FRACTION REPRESENTATION of irrational numbers of degree higher than
2. With the particularity that all this concept was TRIVIALLY devised
by agency of the Rational Mean processes.
Your stupidity, envy, cowardice and psychopathic behavior drived you
to fall in such a rat-trap which has been specially settled for
overbearing ignorants like you. So anything you want to tell about
such GCF is automatically applied to Daniel Bernoulli's method.
Now, you want me to explain to you how the Lineal Homogeneous
Recurrence Relations of Daniel Bernoulli's method works with complex
numbers. WRONG, take a book by yourself and learn that method, and
slow down your overbearing ignorance.
Based on the above considerations, I face and maintain what follows
and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
sttsc...@tesco.net
> On 27 jul, 09:54, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
>
> Now, you want me to explain to you how the Lineal Homogeneous
> Recurrence Relations of Daniel Bernoulli's method works with complex
> numbers.
I know how Bernoulli's single dominant
zero method works.
What I want to know is how your
GCFs which according to you are based
on the rational mean can produce
approximations to a complex root.
What you are claiming is that there are
integers p,q that approximate a complex number
p/q a.e. 1 +i*sqrt(2)
How is this possible ?
arithmonic
wrote:
[CUT more on his nonsense attacks ad-hominen because he is absolutely
unable to find any precedent on the methods shown in my webpages]
SUMMARY:
--------------------------------------------------------
***************************************************
1.- You failed to present any precedents on the new simple methods
based on the Rational Mean:
http://mipagina.cantv.net/arithmetic/rmdef.htm
Which is the very essence of my first posting, so they were forced to
try to rise many other issues and false statments to hide their
incapacity and rash comments on this matter.
***************************************************
2.- You failed in trying to divert the issue on root-
solving to the issue on philology and gramatical use of the phrase :
"GENERALIZED CONTINUED FRACTION".
The phrase: "GENERALIZED CONTINUED FRACTION" does not stand
exclusively for
those continued expressions who yield simultaneous Diophantine
approximations (general pell's equation)
as you falsely alleged, that's another false statement from yours.
That's another lie from yours.
All the readers can find full info on this topic on GCF at (page 3-4,
Section 1.1.1):
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
>From there, you can see that you have no idea on what the phrase GCF
really means,
you have just unsuccessfully tried to cause confusion and attack me ad-
hominen.
You also didn't know that one of the most important characteristics of
the very
particular sample on GCF shown in the webpage:
http://mipagina.cantv.net/arithmetic/gencontfrac.htm
IS THAT SUCH GCF IS JUST A GENERALIZED REPRESENTATION OF DANIEL
BERNOULLI'S
METHOD FOR ROOT-SOLVING, which at the same time is es PERIODIC
CONTINUED-
FRACTION REPRESENTATION of irrational numbers of degree higher than
2.
With the particularity that all this concept was TRIVIALLY devised
by agency of the Rational Mean processes.
Anything you want to tell about such GCF is automatically applied to
Daniel Bernoulli's method.
Now, you want me to explain to you how the Lineal Homogeneous
Recurrence Relations of Daniel Bernoulli's method works with complex
numbers. WRONG, take a book by yourself and learn that method, and
slow down your overbearing ignorance.
Your stupidity and envy drived you to fall in such a continued-rat-
trap which has been specially settled for
overbearing ignorants like you.
***************************************************
3.- You failed to present any posting from mine stating: "My methods
always yield ALL THE BEST APPROXIMATIONS". They were challenged to do
that but failed.
***************************************************
4.- You failed your attempts to discredit the new extremely simple
high-
order arithmetical algorithms by arguing that they do not produce
best
approximations (which is of course another lie from yours that anyone
can
confirm by reading my wepages).
Of course,I have never said in any posting from mine nor in my webpage
and book that these new methods "ALWAYS produce ALL the best
approximants",
that's another lie from yours. You are just a liar trying to cause
confusion.
Notwithstanding, the issue on Best-Approximations is by no means a
requisite for classifying these new methods as true root-solving
algorithms.
Any true root-solving algorithm only need to converge towards the root-
value according to the standard convergence criteria.
Your only intention is to create confusion. What really matters here
is not about if you are an ignorant
but about your unethical behavior and your attacks not only against me
but
against people who do not inhabit this list (http://mipagina.cantv.net/
arithmetic).
I think you should be investigated, indeed, because if you are
teaching mathematics at some school
(I really don't think so but it might be) then educational authorities
should take care about your unethical behavior.
***************************************************
5.- You have not only failed all your attempts but, at the same time,
showed a shameful unethical and
psychopathic behavior and huge cheeks.
***************************************************
END OF SUMMARY
-----------------------------------------------------------------------
NOTES ON YOUR ATTACKS AD-HOMINEN AND YOUR UNETHICAL BEHAVIOR:
Notice that I have spent some time in explaining some points here just
because of all those young people
who inhabit this newsgroup, indeed, I think you are far beyond any
help, indeed. I even feel pity for you and
your friend, as well as I did for some few others in the past.
You have failed again. Your attacks ad-hominen have been demoslished
by the new GENERAL RATIONAL MEAN CONCEPT.
Now, you have to face your unethical behavior.
You have accused me of having no idea about the meaning of the phrase
GCF, you have assaulted
me in so many ways and called me "liar" without signing any single
insulting posting from yours.
It is clear that You have entered to this thread with the only
intention of creating confusion and attacking me by many ways,
just because you are incapable of showing to the sci.math audience any
single precedent on the new hig-order arithmetical algorithms
shown in my webpages. Now, your cowardly behavior starts to face the
consequences of your nonsense attacks against me.
You should cogitate on the fact that neither you nor your friends WILL
BE ABLE TO STOP THESE NEW SIMPLE METHODS.
You will not be able to prevent people from reading them. Neither you
nor any of your friends will be able to stop this.
These new methods and their scope are far beyond any unsuccessful
attacks and insults from yours. They are far beyond you
and your friends or anyone else.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
> I wonder if XXXXXXXXX XXXXX still thinks your contribution to
> mathematical knowledge is still quite so fantastic.
For God sake. You have finally shown the true reason for your
insanity.
Your problem is just a matter of envy, jealousy, etc.
Well, you are far beyond any help, indeed.
The main point here is neither about any person named XXXXXXX XXXX,
nor about whoever could find
of some interest those methods, nor about a me (on the contrary, I
did
not consider such methods as "my methods" even when sometimes for the
sake of brevity I am forced to use such words).
The main point here is about something that you are so far to
understand.
You are far beyond help.
On 26 jul, 22:16, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
wrote:
>...who but a retard would wriite it down for posterity ?
Why don't you meet the people you are cowardly insulting behind your
computer?
http://mipagina.cantv.net/arithmetic
***************************************************************************
***************************************************************************
I am sure you have no courage to continue all your insane insults --
face to face-- against me and
all those people who have wrote something about my methods. You have
no courage to put your signature
and name along with all your insane insults. You have no courage
because your only intention is to try to cause
confusion about the methods shown in my webpages, just because you are
unable to show any sinple precedent on them,
since Babylonian times up to now.
***************************************************************************
***************************************************************************
Based on the above considerations, I face and maintain what follows
and will always do:
******** DEDICATED TO ALL YOUNG MATH STUDENTS ******************
It is just disturbing to realize these so simple arithmetical methods
DO NOT APPEAR in any book on numbers since ancient times up to now:
http://mipagina.cantv.net/arithmetic/rmdef.htm
References and links can be found at:
http://mipagina.cantv.net/arithmetic
THESE SO SIMPLE METHODS 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.
sttsc...@tesco.net
Are you back again, Dumbingo ?
I can't believe that they let loonies like you
run around free in Venezuela.
How can an "engineer" believe that complex
numbers are "tricks and patches" ?
Your mental retardation beggars belief.
What is particularly amusing is that you
claim that complex numbers are "tricks and patches"
yet claim the rational mean method can converge to
a complex root via Bernoulli's single domimant
zero method.
Have you the slighest idea what you are tallking about ?
arithmonic
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]
>
> You are truly a lamentable fool and liar.
>
> You claim in the posting that I cite that
> the rational mean is the basis for all continued fractions
> and generalized continued fractions.
>
> 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.
All the readers can find information on this topic on GCF at (page
3-4, Section 1.1.1):
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
Anyone can see that the phrase: "GENERALIZED CONTINUED FRACTION" does
not stand exclusively for those continued expressions who yield
simultaneous Diophantine
approximations (general pell's equation)
as you falsely alleged, that's another false statement from yours.
You need to lie as well as to insult and attack me just because you
are absolutely unable to find any precedent on the EXTREMELY SIMPLE
HIGH-ORDER ARITHMETICAL METHODS shown in my webpages.
You failed in your attempts of causing confusion, and of course, the
very reason for your attacks is that you hate so much to see a South-
American telling you that: "It is a real shame that such extremely
trivial HIGH-ORDER ARTIHMETICAL METHODS (which embraces Halley's,
Newton's, householder's methods) do not appear in any book on numbers
since Babylonian times up to now.
However, you have no choice but to swallow it.
Eat it and digest it.
Why did you stop your insults against all people who have wrote
something about my methods?
Swallow this:
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
Come on, continue by insulting the author of such book (and other
related people).
Come on, persistent offender.
arithmonic
> > On 26 jul, 04:37, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> > wrote:
> > [cut sick and cowardly behavior hiding his name]
>
> You are truly a lamentable fool and liar.
>
> You claim in the posting that I cite that
> the rational mean is the basis for all continued fractions
> and generalized continued fractions.
>
> 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).
>
> slighest idea of the implications of what you write.
All the readers can find information on this topic on GCF at (page
3-4, Section 1.1.1):
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
Anyone can see that the phrase: "GENERALIZED CONTINUED FRACTION" does
not stand exclusively for those continued expressions who yield
simultaneous Diophantine
approximations (general pell's equation)
as you falsely alleged, that's another lie from yours.
You need to lie as well as to insult and attack me just because you
are absolutely unable to find any precedent on the EXTREMELY SIMPLE
HIGH-ORDER ARITHMETICAL METHODS shown in my webpages:
http://mipagina.cantv.net/arithmetic/rmdef.htm
You failed in all your attempts of causing confusion. Considering that
you are now bringing out the name of my Country, it is clear that you
hate so much to see a South-American telling you that: "It is a real
shame that such extremely trivial HIGH-ORDER ARTIHMETICAL METHODS
(which embraces Halley's, Newton's, householder's methods) do not
appear in any book on numbers since Babylonian times up to now.
Unfortunatedly and to your disgrace, you have no choice but to swallow
it.
Eat it and digest it. You CANNOT stop these NEW HIGH-ORDER
ARITHMETICAL METHODS.
Why did you stop your insults against all people who have written
something about on my methods?
Swallow this:
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
Come on, continue by insulting the author of such book (and other
related people), I am sure that they do not agree with most of my
critics to the root-solving history and I do not want them to do so,
but they are true un-biased mathematicians.
Come on, persistent offender.
Show some precedents on the methods shown in my webpages.
sttsc...@tesco.net
> > > On 26 jul, 04:37, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> All the readers can find information on this topic on GCF at (page
> 3-4, Section 1.1.1):
>
> http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
Dumbingo
What is it that the extract from Finch's book is supposed to
demonstrate ?
"1.1.1 Generalized Continued Fractions
It is well known that any quadratic irrational possesses a periodic
regular continued fraction expansion and vice versa"
This is a false statement. It is not the case that every quadratic
irrational has a periodic RCF expansion. Every quadratic irrational
has a RCF
expansion that is either periodic or eventually periodic.
"Comparatively few people have examined the generalized continued
fraction"
It is not clear which of the "two types" of generalized continued
fraction
Finch is referring to. If he is referring to the "bifurcating" CF then
what he says is true. Basically, all these "bifurcating CFs" are is
pretty patterns on
a page. To generalize simple CFs you have to generalize their
mathematical properties not how they look when written down.
The basic properties of a SCF expansion of a real number t are
1) All best rational approximations to t are produced
2) If t is rational, the SCF expansion terminates
3) if t is a quadratic irrational, the SCF expansion is purely
periodic
if t is a reduced root of an irreducible quadratic equation and
eventually
periodic otherwise.
4) A SCF expansion will indicate if t', a decimal , is an
approximation to a quadratic irrational t
A generalization of the SCF should have at least one of these
properties - say the ability to distinguish between rationals,
quadratic irrationals and cubic irrationals.
If you think of the SCF of t as a sequence of unimodular matrix
transformations applied to a point written using homogeneous
coordinates (t,1), giving a sequence of homogeneous points (t(1),1)
(t(2),1) ...,(t(n),1) periodicity will occur when t(m), t(m+k) are in
the same ratio. In terms of linear algebra t(m), t(m+k), ....are fixed
points (or eigenvectors) of powers of a unimodular matrix.
If you want periodicity to occur when considering say cubic
irrationals , you must consider a point of the form (s,t,1).
(s and t must ,of course, belong to the same cubic field). In other
words
you must have a "2-dimenesional" CF.
The Gupta-Mittal CF referred to by Finch is in fact of this form, but
no general law of formation for convergents is stated.
The Gupta-Mittal CF for two reals a, b is based on these equations
A(i) = int(a(i))
B(i) = int)b(i))
a(i+1) = 1/(b(i) -B(i))
b(i+1) = (a(i) -A(i))/(b(i) -B(i))
But this is essentially, a Jacobi-Perron -type continued fraction/
Gupta and Mittal seem to think that the SCF is "defective" in some way
as the SCF expansions of higher irrationals are not periodic.
The situation is actually the reverse. The SCF has optimal properties.
The difficulty is finding generalizations that have at least one of
the SCF's
desired properties.
Given a real number or a set of real numbers, the Dumbingo CF
cannot discover to what degree of irrationality they belong unless
their
algebraic equations are known beforehand. It doesn't produce best
approximations
Another intellectual triumph for Dumbingo Gormless Moron
arithmonic
wrote:> > All the readers can find information on this topic on GCF at pages 3-4, Section 1.1.1):
> >http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
>
> What is it that the extract from Finch's book is supposed to
> demonstrate ?
Now, you don't know what all this means. let's see:
*************************************************
*************************************************
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 ?
*************************************************
*************************************************
This time you didn't insult the author of the link:
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
He also use the name "Generalized Continued Fractions" for
my periodical high-order expressions.
Why you didn't insult him this time?
Why you didn't call him retard this time?
Why you raised the name of my country in your last posting?
There are many reasons for all that:
1.- You are a coward that thinks that you can insult any Southamerican
guy the way you want. You think that you can be a persistent offender
and nothing will happen just because it is
just a LatinAmerican guy.
That's the main reason you are not willing to insult him (and many
others from other countries) but prefer to insult the LatinAmerican
guy and tell lies about his work.
2.- The other reason is that you really HATE, so much, to see this
SouthAmerican guy telling you these truths about the whole history of
roots solving, and teaching you these new extremely simple high-order
methods, mainly, when considering that you are incapable of showing
any single precedent on them since Babylonian times up to now.
It is a real disgrace for you to be forced to swallow all this, mainly
when considering that you have been crushed just by a Civil Engineer,
not a mathematician. So, I understand how low is your selfsteem-level
by this time, that's why you desperately need to insult and act as a
persistent offender.
Notice that you have been crushed by a humble SouthAmerican Civil
Engineer in such a way that you had no other chance but to bring out a
discussion on the way you demand that the phrase "Generalized
Continued Fractions" should be used.
In his book:
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
The author clearly states what the meaning of the phrase "Generalized
Continued fractions" is all about.
It is clear that other people even decided to use other very different
names for their generalized expressions. Standard Continued
Fractions have so many properties, if you can find any high-order
generalization for any of those properties then you are free to use
the phrase GCF, that's it. in my case the property is: Periodic
representation of irrational numbers of higher degree.
You are clearly unable to realize that I don't care about the
transcendence of such very particular GCF expression shown in my
webpages, because there are many others, and that is not the true
issue of my work.
You said:
>"It is not clear which of the "two types" of generalized continued
fraction Finch is referring to."
You have been finally crushed and forced to admit that there can be
various types of generalized continued fraction.
You are not the "choosen" who will decide how to use mathematical
phrases. You have been crushed and forced to slow your overbearing
ignorance down.
That is what my posting demonstrate.
--------------------------------------------------------
Just swallow what follows very gently, again and again:
sttsc...@tesco.net
> On 6 ago, 13:35, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
>
> > On 6 Aug, 15:18, arithmonic <djes...@gmail.com> wrote:
> > > All the readers can find information on this topic on GCF at pages 3-4, Section 1.1.1):
> > >http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
>
> > What is it that the extract from Finch's book is supposed to
> > demonstrate ?
>
> Now, you don't know what all this means. let's see:
Dumbingo
I see you don't know what it means, yet you quote it.
Try an explanation rather than the usual production of wind.
> This time you didn't insult the author of the link:http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
No I prefer to insult you, you pompous buffoon.
> Why you didn't insult him this time?
> Why you didn't call him retard this time?
I corresponded with Finch some years ago.
He is not a deluded wind-bag ke you.
> Notice that you have been crushed by a humble SouthAmerican Civil
> Engineer
Overbearinghly humble and with much to be humble about.
Young student, be sure there is something very wrong with Dumbingo
Gormless Moron, the ranting crackpot from Caracass
mike3
wrote:
> Are you back again, Dumbingo ?
>
> I can't believe that they let loonies like you
> run around free in Venezuela.
>
What's so bad about letting him run around free?
It's just math for crying out loud. So what if
he comes up with a dumb, bad piece of math? Math
is all in the head, how is it going to KILL
somebody?
mike3
> Come on, continue by insulting the author of such book (and other
> related people), I am sure that they do not agree with most of my
> critics to the root-solving history and I do not want them to do so,
> but they are true un-biased mathematicians.
>
> Come on, persistent offender.
>
> Show some precedents on the methods shown in my webpages.
Ignore the guy's childish insults, drop your
OWN childish insults and RESPOND TO HIS POINT:
"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). "
Can you do that, with LOGIC?
sttsc...@tesco.net
> On Aug 5, 5:03 pm, "sttscitr...@tesco.net" <sttscitr...@tesco.net>
> wrote:
>
> > Are you back again, Dumbingo ?
>
> > I can't believe that they let loonies like you
> > run around free in Venezuela.
>
> What's so bad about letting him run around free?
someone who has graduated from university, thinks that
complex numbers are "tricks and patches" . It's a bit like
a doctor claiming that there is no such thing as viruses.
He denounces people like Grover Hughes (my secret co-conspirator)
simply because he dares to question Dumbingo's "God-like" authority
in these manners. Dumbingo's rants always have the same format and
haven't changed in years. I was wondering when he would bring up the
"humble South American civil engineer" line. He seems to think that
there is some "Cartesian-decimal" conspiracy ranged against him,
although in all the yeras I have been winding him up, he has never
been able to explain what that might mean.
Maybe I should be taking Dumbingo more seriously
and someone with a brain could interpret in a more comprehensible
manner what he is trying to say.
After all, he is the one making the all the claims.
If he doesn't want to or can't answer legitimate questions,
he shouldn't post.
arithmonic
> On 6 Aug, 15:18, arithmonic <djes...@gmail.com> wrote:
> > All the readers can find information on this topic on GCF at pages 3-4, Section 1.1.1):
> >http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
> What is it that the extract from Finch's book is supposed to
> demonstrate ?
Now, you don't know what all this means. let's see:
*************************************************
*************************************************
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 ?
*************************************************
*************************************************
This time you decided not to continue by insulting those people who
have written something about my work, in this case you didn't insult
the author of the link:
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
He also use the name "Generalized Continued Fractions" for my
periodical high-order expressions.
He asserts that can be various types of "Generalized Continued
Fractions" according to the very specific CF property that has been
generalized.
Why you didn't continue by insulting him this time?
Why you didn't continue by calling him retard this time?
You certainly said:
>...who but a retard would wriite it down for posterity ?
Why are you so coward?
Why you raised the name of my country in your last posting?
There are many reasons for all that:
1.- You are a coward that thinks that you can insult any
Southamerican
guy the way you want. You think that you can be a persistent offender
and nothing will happen just because it is
just a LatinAmerican guy.
That's the main reason you are not willing to insult him (and many
others from other countries) but prefer to insult the LatinAmerican
guy and tell lies about his work.
2.- The other reason is that you really HATE, so much, to see this
SouthAmerican guy telling you these truths about the whole history of
roots solving, and teaching you these new extremely simple high-order
methods, mainly, when considering that you are incapable of showing
any single precedent on them since Babylonian times up to now.
It is a real disgrace for you to be forced to swallow all this,
mainly
when considering that you have been crushed just by a Civil Engineer,
not a mathematician. So, I understand how low is your selfsteem-level
by this time, that's why you desperately need to insult and act as a
persistent offender.
Notice that you have been crushed by a humble SouthAmerican Civil
Engineer in such a way that you had no other chance but to bring out
a
discussion on the way you demand that the phrase "Generalized
Continued Fractions" should be used.
The author clearly states what the meaning of the phrase
"Generalized
Continued fractions" is all about.
The very particular "Generalized Continued Fractions" developed by
agency of the Rational Mean and shown in my webpages do not bring a
solution for the general pell's equation, and neither I nor my
webpages, nor any posting from mine states that they do such thing.
They only bring a Generalization of Periodical Representation or high-
order irrational numbers, that is fairly clear stated in my webpages,
and you certainly know that, but you just want to talk about your lies
on that matter.
Standard Continued Fractions have so many properties, if you can find
any high-order
generalization for any of their properties then you are free to use
the phrase GENERALIZED CONTINUED FRACTION , because you have found a
very particular generalization os stantard continued fractions, that's
it. in my case the property is: Periodic
representation of irrational numbers of higher degree.
You are clearly unable to realize that I don't care about the
transcendence of such very particular GCF expression shown in my
webpages, because there are many others generalizations that can be
obtained by agency of the Rational Mean, and that is not the true
issue of my work.
You said:
>"It is not clear which of the "two types" of generalized continued
fraction Finch is referring to."
You have been finally crushed and forced to admit that there can be
various types of generalized continued fraction.
It seems that you think about yourself as a kind of "choosen" who will
decide how to use mathematical phrases. You have been crushed and
forced to slow your overbearing
lies down.
That is what my posting demonstrate. Also it demonstrates that you do
not want to talk about those extremely simple arithmetical "root-
solving" methods (which is the very spine of ALL my postings), but
just want to deviate the issue to "best approximations" and pell's
equation and the use of the phrase "GCF".
--------------------------------------------------------
Just swallow what follows very gently, again and again, because this
is what I have said all through my postings in many newsgroups, and
that is precisely all what you want do not want to discuss by any
means:
arithmonic
wrote:
> Don't you think it's a bit odd that a trained engineer,
> someone who has graduated from university, thinks that
> complex numbers are "tricks and patches" . It's a bit like
> a doctor claiming that there is no such thing as viruses.
For God sake, your overbearing Cartesian-Decimal delutions have also
drived you to think that imaginary numbers are actually alive in the
same way as virusses are.
When did you begin to realize that imaginary numbers were actually
alive?
Do you talk to them very often?
Man, what a crank, inded. What a loony.
Try to find a girl, to drive a car, to dig a cave, try something, man,
the sooner the best.
arithmonic
What make you think that you are the one who can impose what the scope
of the phrase "GCF" is?
or what such phrase means?
You and the other guy did not put your signatures on your postings
while the author of the following book certainly did. What make you
think that your comments are worth of any consideration?
In his book:
http://assets.cambridge.org/052181/8052/sample/0521818052ws.pdf
The author clearly states what the meaning of the phrase
"Generalized Continued fractions" is all about.
The very particular "Generalized Continued Fractions" developed by
agency of the Rational Mean and shown in my webpages do not bring a
solution for the general pell's equation, and neither I nor my
webpages, nor any posting from mine states that they do such thing.
They only bring a Generalization of Periodical Representation or
high-
order irrational numbers, that is clearly stated in my webpages, even
with numerical samples.
Standard Continued Fractions have so many properties, if you can find
any high-order generalization for any of their properties then you are
free to use
the phrase GENERALIZED CONTINUED FRACTION , because you have found a
very particular generalization os stantard continued fractions,
that's
it. in my case the property is: Periodic
representation of irrational numbers of higher degree.
ing. Domingo Gomez Morin
Structural Engineer
Caracas
Venezuela
sttsc...@tesco.net
The following are very good approximations to
two algebraic numbers. It should be a simple
matter to find their periodic GCF expansions and
determine what kind of irrationalities they are
(perhaps 24th roots of two natural numbers).
I'm presuming, of course, the decimals won't be
too difficult for you.
1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798968725339654633180882964062061525835239505474575028775996172983557522033753185701135437460340849884716038689997069900481503054402779031645424782306849293691862158057846311159666871301301561856898723723528850926486124949771542183342042856860601468247207714358548741556570696776537202264854470158588016207584749226572260020855844665214583988..
2.658967081916994079346775156784015615243993344562777100352215488984168020780336074844290784427693107613067572871690262426374600133746033407625021112602552964870032883932874004774472853345698752169501143322106362939726300008123452158007567812775186248096838112692389402757673009916461344412528792767658269885942868562886921929839475090355553563423870615924022015863882063621474748997441003464872426038019818501626813687256795151622423686801397039164051881841963682851541156279028236193018355642051579528602629780388403586612568303893356087010910049905321214872909130575066776910263489645877681228272722684114645491639412414595390610205782877528690733015537261962890625..
rich burge
> On Aug 6, 8:18 am, arithmonic <djes...@gmail.com> wrote:
>
> > Come on, continue by insulting the author of such book (and other
> > related people), I am sure that they do not agree with most of my
> > critics to the root-solving history and I do not want them to do so,
> > but they are true un-biased mathematicians.
>
> > Come on, persistent offender.
>
> > Show some precedents on the methods shown in my webpages.
>
> Ignore the guy's childish insults, drop your
> OWN childish insults and RESPOND TO HIS POINT:
>
> "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.
It is not at all clear to me that this is possible. See the paper
"Best Simultaneous Diophantine Approximations II. Behavior of
Consecutive Best Approximations" by J.C. Lagarias. It seems as
though something has to be relaxed in the generalization.
> 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). "
>
Finding solutions to the cubic Pell is easy (use Pari/gp). Proving
(unconditionally) the solution you find is, say, the fundamental
solution can take a bit more effort.
> Can you do that, with LOGIC?
Rich Burge
Slurry Dawg
Cool, CA
USA
sttsc...@tesco.net
> On Aug 7, 3:06?pm, mike3 <mike4...@yahoo.com> wrote:
>
> > On Aug 6, 8:18 am, arithmonic <djes...@gmail.com> wrote:
> > "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.
>It is not at all clear to me that this is possible.
Yes, that's the point. The OP was claiming that
he had invented a form of generalized continued fraction
the produced best simultaneous ? rational approximations
and was periodic for higher irrationalities.
It turns out that he was not claiming that he could produce
all best rational approximation but simply that
the occasional best approximation might occur among the
"convergents".
He now says that his GCFs produce periodic expansions of
higher irrationalities in some way based on
Bernoulli's dominant zero method.
But this is not what is usually meant by
periodicity. If every algebraic number has a "periodic
expansion" in the sense that it is some function of the
coefficients of its characteristic polynomial, then
there is no way of discriminating between irrationalities
of various degrees.
Essentially, all the OP is doing is expressing
the ratio of the nth and n-1th terms in a recurrence relation
as a complicated fraction involving the coefficients
of the characteristic polynomial.
I would not have thought that this approach would produce periodicity,
except in this trivial sense, or any best rational approximations.
Finding solutions to the cubic Pell is easy (use Pari/gp).
Do you mean systematically using generalizations of continued
fractions or
other methods for finding cubic units or just intelligent
trial and error ?
Proving (unconditionally) the solution you find is, say, the
fundamental
solution can take a bit more effort.
Yes, I saw your recent post and Israel's interesting answer.
Have you found some way of estimating an upper bound
for the power of the unimodular matrix so that you can
find the fundamental unit after a small number of trials ?
rich burge
wrote:
>
> Finding solutions to the cubic Pell is easy (use Pari/gp).
>
> Do you mean systematically using generalizations of continued
> fractions or
> other methods for finding cubic units or just intelligent
> trial and error ?
>
What I had in mind was something like this:
(12:39) gp > ?bnfinit
bnfinit(P,{flag=0},{tech=[]}): compute the necessary data for future
use in
ideal and unit group computations, including fundamental units if they
are not
too large. flag and tech are both optional. flag can be any of 0:
default, 1:
insist on having fundamental units, 2: do not compute units, 3: small
bnfinit,
which can be converted to a big one using bnfmake. See manual for
details
about tech.
(12:39) gp > a=bnfinit(X^3-25,1);
(12:39) gp > a.fu
%34 = [Mod(4/5*X^2 - 2*X - 1, X^3 - 25)]
(12:41) gp > p3(k,x,y,z)=x^3+k*y^3+k^2*z^3-3*k*x*y*z
(12:41) gp > p3(25,-1,-2,4/5)
%35 = -1
I also have a homebrewed method for finding solutions that is pretty
fast (it finds a 30000+ digit solution for k=1000700 in less than a
minute) but comes without any guarantees about the solution being
fundamental. Pari is much faster, more general, and comes with a
conditional guarantee.
> Proving (unconditionally) the solution you find is, say, the
> fundamental
> solution can take a bit more effort.
>
> Yes, I saw your recent post and Israel's interesting answer.
> Have you found some way of estimating an upper bound
> for the power of the unimodular matrix so that you can
> find the fundamental unit after a small number of trials ?
No, not really. Moveover, given any reasonable definition of "a small
number of trials" I believe it is possible to show the approach I had
in mind does not work. I have not played with it much, however.
Here is a link to an article on this subject you may find interesting:
Determining the Fundamental Unit of a Pure Cubic Field Given Any Unit
N. S. Jeans; M. D. Hendy
Mathematics of Computation, Vol. 32, No. 143. (Jul., 1978), pp.
925-935.
Stable URL:
http://links.jstor.org/sici?sici=0025-5718%28197807%2932%3A143%3C925%3ADTFUOA%3E2.0.CO%3B2-0
Rich
sttsc...@tesco.net
I'm not familiar with Pari/gp, but there are methods using
the regulator and cycles of ideals that always find
fundametal units. Aren't they decribed in Cohen's book ?
What's the basic idea ? Isn't this a long way from (vector)
continued fraction algorithms ?
> I also have a homebrewed method for finding solutions that is pretty
> fast (it finds a 30000+ digit solution for k=1000700 in less than a
> minute) but comes without any guarantees about the solution being
> fundamental.
Yes, you have mentioned this before, but were not specific.
Didn't you say it was a probabilistic version of Jacobi -erron ?
> > Yes, I saw your recent post and Israel's interesting answer.
> > Have you found some way of estimating an upper bound
> > for the power of the unimodular matrix so that you can
> > find the fundamental unit after a small number of trials ?
>
> No, not really. Moveover, given any reasonable definition of "a small
> number of trials" I believe it is possible to show the approach I had
> in mind does not work. I have not played with it much, however.
>
> Here is a link to an article on this subject you may find interesting:
>
> Determining the Fundamental Unit of a Pure Cubic Field Given Any Unit
> N. S. Jeans; M. D. Hendy
> Mathematics of Computation, Vol. 32, No. 143. (Jul., 1978), pp.
> 925-935.
Thanks, that looks very interesting.