Find square root using Monte carlo?

derive numerical value of square root of 2 using MC

[James Tursa]

Were you given any more instructions in the assignment? What have you done so far?

[John D'Errico]

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.

Answer 1

[Brandon]

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)...?

Answer 2

[Walter Roberson]

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.

[Atishay Jain]

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!

[Walter Roberson]

N = 100000;
approximation = mean((rand(1,N)*2).^2 <= 2)

approximation = 0.7081

square_root_2 = approximation * 2

square_root_2 = 1.4162

square_root_2 * square_root_2

ans = 2.0055