jeffies, I knew how to use newton to *****approximate***** square roots using
an ADDING MACHINE several decades ago.

That was not the question.

Go back and read the question AGAIN, this time ask your wife to help you.

Well, I said this would be too complicated for jaxie to understand. Newton's
method converges quickly and can easily be worked to the desired accuracy,
just
like the normal method for doing long division.

Sorry jaxie, as for square roots, one math lesson a day is all I'm willing to
give someone incapable of learning. OK, you can just iterate on:
x2 = x1 - (x1^2 - a)/(2 * x1)
A tad more tedious than the method taught in high school, but easier to
program.



"JAXAshby" wrote in message
...
jeffies, that is NOT algebraic. Ask your wife to explain the term to you.

a bit of a hint for you jeffies. algebraic would give you precision to as
many
decimals was you might wish to calc with accuracy to the next to last digit
calc'd.

go ahead. tell us how to do that with a pencil and paper. Tell you what.
Tell us how to do square roots *algebraically* with a pencil and paper.

ask your wife to explain square roots.

Well, I wouldn't say its so easy that jaxie can follow, but there are all
sorts
of techniques that have been developed over the years. Computers don't
use
"magic" to calculate complex functions, there are often just programmed to
follow algorithms developed many years ago by people like Newton. Jaxie
forgets
that this is what I did for a living.

To compute a 4th root, using Newton's method:

Assume you want to compute x = a^(1/4)
Make a guess at the answer, call it x1. Then compute the next guess, x2,
as
follows:
x2 = x1 - (x1^4 - a)/(4 * x1^3)
iterate again as
x3 = x2 - (x2^4 - a)/(4 * x2^3)

When the results get sufficiently close, you have an answer. Often only 3
or
4
iterations are needed. Similar techniques can be used to calculate the
roots
of
polynomials.

I used the square root version of this a number of times. In the days
before
"Floating Point Units" in computers considerable time savings (a factor of
10
or
more) could be had by adjusting the algorithms to match the input data
and
desired accuracy.




"JAXAshby" wrote in message
...
wanna show us how?

]okay group, watch now how jeffies blathers on for days telling us that
what
with his degree in physics and all that he can do it easily. if I say
he
can
not he will get all snippy. he couldn't tell us how RDF worked how is
he
going
to tell us how to do 4th roots with pencil and paper.]

jeffies? do note the word algebraicly was there. in other words,
SWAGing
is
not the answer.

What's so hard about doing 4th roots with pencil and paper?



"JAXAshby" wrote in message
...
bull. there is no intuitive way to calculate the product of those
numbers
in
that way, any more than you can calc a 4th root of a number
algabraicly
with a
pencil and paper.