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-   -   Square root formulas (http://mymathforum.com/elementary-math/345578-square-root-formulas.html)

mones January 3rd, 2019 11:09 PM

Square root formulas
 
I deduced a simpler formula for the square root using only one trigonometric function "acos", it is a controllable precision formula in advance, the correct decimals 2n are controlled by choosing n, based on the discovery of a pattern, the square root is proportional to the angle:

√x=1/(10^n acos⁡[x/(x+0.5 10^(-2n) )] )
or
√x= 10^n x acos⁡[x/(x+0.5 10^(-2n) )]

Because "acos" is ill-conditioned I suggest to use a high precision program to calculate the formula such as

https://www.wolframalpha.com/

You can check my research paper preprint at :

https://www.researchgate.net/profile/Mones_Jaafar

I welcome your comments and hope that you find it useful

mathman January 4th, 2019 12:53 PM

Why is this better than usual methods?

v8archie January 4th, 2019 02:17 PM

what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$

romsek January 4th, 2019 03:51 PM

Quote:

Originally Posted by v8archie (Post 604101)
what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$

yeah

mones January 4th, 2019 10:08 PM

1 Attachment(s)
Quote:

Originally Posted by mathman (Post 604100)
Why is this better than usual methods?

You can calculate the square root without iterations or calculations steps, by simply replacing x and choosing n according to your need
You can control the correct decimals by simply choosing n

if you choose n = 3 you get 2n = 6 correct decimals
if you choose n = 18 you get 2n= 36 correct decimals

The formulas are based on the discovery of a pattern

this is not a calculation method only it is a mathematical law and formulas that illustrate the incontestable relation between the square root and the trigonometric function according to a specific pattern,


Thanks,

mones January 4th, 2019 10:12 PM

1 Attachment(s)
Quote:

Originally Posted by v8archie (Post 604101)
what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$

Yes, exactly
to calculate the square root of x choose n that control the correct decimals 2n and calculate the formula using a correct and high precision program such as
https://www.wolframalpha.com/

mones January 4th, 2019 10:14 PM

Quote:

Originally Posted by romsek (Post 604102)
yeah

I did not understand your comment can you clarify please?

romsek January 4th, 2019 10:20 PM

Quote:

Originally Posted by mones (Post 604108)
I did not understand your comment can you clarify please?

I was answering Archie

mathman January 5th, 2019 01:19 PM

Quote:

Originally Posted by mones (Post 604106)
You can calculate the square root without iterations or calculations steps, by simply replacing x and choosing n according to your need
You can control the correct decimals by simply choosing n

if you choose n = 3 you get 2n = 6 correct decimals
if you choose n = 18 you get 2n= 36 correct decimals

The formulas are based on the discovery of a pattern

this is not a calculation method only it is a mathematical law and formulas that illustrate the incontestable relation between the square root and the trigonometric function according to a specific pattern,


Thanks,

You still need to calculate acos, which is not easier than square root iteration.

topsquark January 5th, 2019 03:19 PM

Quote:

Originally Posted by mathman (Post 604126)
You still need to calculate acos, which is not easier than square root iteration.

I know very very little about this but I think the OP is talking about on a computer.
Quote:

... I suggest to use a high precision program to calculate the formula...
-Dan


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