I need to find the area of a circle using the monte carlo method the twist is i need to generate random points until the number that lie outside reach a specified number ie. 4*(#inside​/inside+ou​tside)=pi

I need to count the points that fall outside and inside and not stop till the number outside reach a specified number

[John Chilleri]

You can do this using a while loop.

while (4*(in/(in+out)) ~= pi)
      % random point
      % update in/out appropriately
end
% determine area approximation

Although I imagine continuing till it equals pi could cause problems, I would do something along the lines of:

while (abs(4*(in/(in+out)) - pi) > 1e-6)
      % random point
      % update in/out appropriately
end
% approximate area

This will instead continue to apply Monte Carlo until your condition is roughly 5 decimal digits accurate to pi.

Hope this helps!

Answer 1

[Image Analyst]

Try this:

R = 1;
numInside = 0;
numOutside = 0;
maxOutsideCount = 100000; % Whatever you want...
loopCounter = 0;
while numOutside < maxOutsideCount
  x = rand;
  y = rand;
  r = sqrt(x^2+y^2);
  if r < R
    numInside = numInside + 1;
  else
    numOutside = numOutside + 1;
  end
  loopCounter = loopCounter + 1;
end
fprintf('Exited after %d points: %d inside and %d outside.\n', ...
  loopCounter, numInside, numOutside);

Adapt as needed.