My Math Forum Square root formulas

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 January 3rd, 2019, 11:09 PM #1 Newbie   Joined: Dec 2018 From: syria Posts: 10 Thanks: 0 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
 January 4th, 2019, 12:53 PM #2 Global Moderator   Joined: May 2007 Posts: 6,732 Thanks: 689 Why is this better than usual methods? Thanks from topsquark
 January 4th, 2019, 02:17 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,640 Thanks: 2624 Math Focus: Mainly analysis and algebra what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$ Thanks from topsquark
January 4th, 2019, 03:51 PM   #4
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Quote:
 Originally Posted by v8archie what does x/(x+0.5 10^(-2n) ) mean? Is it $$\frac{x}{x+0.5 \times 10^{-2n}}$$
yeah

January 4th, 2019, 10:08 PM   #5
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Quote:
 Originally Posted by mathman 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,
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January 4th, 2019, 10:12 PM   #6
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Quote:
 Originally Posted by v8archie 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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 Formulas.jpg (9.6 KB, 1 views)

January 4th, 2019, 10:14 PM   #7
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Quote:
 Originally Posted by romsek yeah

January 4th, 2019, 10:20 PM   #8
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Quote:
 Originally Posted by mones I did not understand your comment can you clarify please?

January 5th, 2019, 01:19 PM   #9
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Quote:
 Originally Posted by mones 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.

January 5th, 2019, 03:19 PM   #10
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Quote:
 Originally Posted by mathman You still need to calculate acos, which is not easier than square root iteration.
Quote:
 ... I suggest to use a high precision program to calculate the formula...
-Dan

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