Find square root using Monte carlo?

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RSR
RSR on 19 May 2015
Commented: Atishay Jain on 21 Feb 2018
derive numerical value of square root of 2 using MC
  2 Comments
John D'Errico
John D'Errico on 19 May 2015
Easy peasy. For example, to find the square root of 2...
X = 2;
Xroot = 1;
while Xroot.^2 ~= X
Xroot = X*rand;
end
When it converges, you are done. Of course, that may take some serious time. Just thinking, but I'm wondering just how many completely unworkable (but in theory, valid) answers I can think of for this problem? I'll bet I can think of at least a few more.
If you want a better answer, you will need to make more effort than simply posting your assignment.

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Answers (2)

Brandon
Brandon on 19 May 2015
This sounds like a homework assignment, so nobody here is going to answer it directly for you.
This website might give you some inspiration though: http://mathfaculty.fullerton.edu/mathews/n2003/montecarlopimod.html
In this problem, pi is the unknown value. Let's say you knew pi, would you be able to find another parameter? The answer is yes. Now how do you make that parameter equal to sqrt(2)...?

Walter Roberson
Walter Roberson on 19 May 2015
Generate a random value between 0 and 2. Square it. If the square is <= 2 then add 1 to a counter. Repeat this fixed number of times. The ratio between the counter and the number of times you repeated this will approach sqrt(2)/2.
  1 Comment
Atishay Jain
Atishay Jain on 21 Feb 2018
I can't figure out why it will approach sqrt(2)/2 ... It's not areas of square with side sqrt(2)/ area of square with side 2.
What is it?
Thank you!

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