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January 3rd, 2019, 11:09 PM   #1
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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
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January 4th, 2019, 12:53 PM   #2
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Why is this better than usual methods?
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January 4th, 2019, 02:17 PM   #3
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what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$
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January 4th, 2019, 03:51 PM   #4
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Quote:
Originally Posted by v8archie View Post
what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$
yeah
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January 4th, 2019, 10:08 PM   #5
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Originally Posted by mathman View Post
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,


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January 4th, 2019, 10:12 PM   #6
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Originally Posted by v8archie View Post
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/
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January 4th, 2019, 10:14 PM   #7
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yeah
I did not understand your comment can you clarify please?
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January 4th, 2019, 10:20 PM   #8
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I did not understand your comment can you clarify please?
I was answering Archie
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January 5th, 2019, 01:19 PM   #9
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Quote:
Originally Posted by mones View Post
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.
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January 5th, 2019, 03:19 PM   #10
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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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