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

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 arithmetic Posts: 106 From: venezuela Registered: 1/23/06
Re: cube root of a given number
Posted: Jul 24, 2007 11:12 AM

*************
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

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