Re: Marie Jean Faucounau sues me for at least 8,487 Swiss Fr

From: dgomez (rationalprocess_at_hotmail-dot-com.no-spam.invalid)
Date: 01/11/05 

Date: 11 Jan 2005 15:26:48 -0600

Mr. Franz Gnaedinger,

It is clear you are unable to answer such a simple question.
Just refrain yourself from pasting my name in your postings trying
to relate my work with "your" Bernoulli's sequence for the square
root.
Stop by making false statements about me and my work. That's it.
Domingo Gomez Morin
mipagina.cantv.net/arithmetic

> dgomezwrote:
Dear Mr. Franz Gnaedinger,
>
> Your are just talking about the SQUARE ROOT columns,
> 1 ----- 1 ----- 2
> 2 ----- 3 ----- 4
> 5 ----- 7 ---- 10
> .
> .
> I'M ASKING YOU SPECIFICALLY ABOUT THE CUBE ROOT COLUMN :
> (http://www.mathforum.com/epigone/math-history-list/skunclerdsax)
> 1 1 1 2
> 2 2 3 4
> 4 5 7 8
> .
> .
> .
> Could you please, for God sake, answer this simple question.
>
>
> When did you publish the [b]CUBE
ROOT[/b] COLUMN?
> Why do you choose those specific initial integer values: (1,1,1,2)
> and what is the REASON FOR SUCH SUMS AND THE CONVERGENCE to
> the cube root ??.
>
>
> Domingo Gomez Morin
> mipagina.cantv.net/arithmetic

***************************************************
GNAEDINGER WROTE:

--- 1 ----- 1 ----- 2
------- 2 ----- 3 ----- 4
----------- 5 ----- 7 ---- 10
-------------- 12 ---- 17 ---- 24
------------------ 29 ---- 41 ---- 58
---------------------- 70 ---- 99 --- 140 --- and so on

That number column does work. Multiply the first by the
last number of each line: 1x2 = 2, 2x4 = 8, 5x10 = 50,
and so on. Compare them to the square of the central
number of each line: 1x1 = 1, 3x3 = 9, 7x7 = 50, and so
on. The square of the central number is always 1 unit
smaller larger smaller larger smaller larger smaller
larger ... than the product of the numbers on the sides,
and while the absoulte mistake remains always one, the
numbers of the column increase, which means the relative
mistake is diminishing.

When I had established my first number column, back in
1979, I expanded the principle, in late 1993 and early
1994: the same principle works for the lines 1-1-3,
1-1-5, and 1-1-1-2. It also works for the line 1-1-4,
and this case shows how quickly the small-numbered
columns approximate:

--- 1 ----- 1 ----- 4
------- 2 ----- 5 ----- 8
----------- 7 ---- 13 ---- 28
-------------- 20 ---- 41 ---- 80 --- and so on

The ratios 1/1, 5/2, 13/7, 41/20 ... are approximating
the square root of 4, which is 2. The correct ratios
would be 2/1, 4/2, 14/7, 40/20. You can also start with

--- 1 ----- 2 ----- 4
------- 3 ----- 6 ---- 12
----------- 9 ---- 18 ---- 36 --- and so on

In this case you obtain the ratios 2/1, 6/3, 18/9 = 2,
always the correct number.

You can start a number column of mine with any pair of
numbers, for example 1-7-2, and you can make mistakes,
you will nevertheless approximate the root of 2 (in this
case). This means the algorithm is robust. And the
mathematical correctness of my number columns had been
proved by Dr. Christoph Poeppe, editor of the German
version of the Scientific American in 1994 or 95, as
I recall, while he published my method for calculating
pi in the May 1997 issue of the German SciAm, not in
the 1994 issue, as I said in my previous message. Sorry
for that mistake.

Franz Gnaedinger www.seshat.ch
-[/quote][/quote]

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