Monte Carlo Simulation
Calculation of Pi Using the Monte Carlo Method by Eve Andersson
Home : Pi : One Calculation
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The "Monte Carlo Method" is a method of solving problems using statistics. Given the probability, P, that an event will occur in certain conditions, a computer can be used to generate those conditions repeatedly. The number of times the event occurs divided by the number of times the conditions are generated should be approximately equal to P.
How this program works:
If a circle of radius R is inscribed inside a square with side length 2R, then the area of the circle will be pi*R^2 and the area of the square will be (2R)^2. So the ratio of the area of the circle to the area of the square will be pi/4.
This means that, if you pick N points at random inside the square, approximately N*pi/4 of those points should fall inside the circle.
This program picks points at random inside the square. It then checks to see if the point is inside the circle (it knows it's inside the circle if x^2 + y^2 < R^2, where x and y are the coordinates of the point and R is the radius of the circle). The program keeps track of how many points it's picked so far (N) and how many of those points fell inside the circle (M).
Pi is then approximated as follows:
4*M pi = --- N
Although the Monte Carlo Method is often useful for solving problems in physics and mathematics which cannot be solved by analytical means, it is a rather slow method of calculating pi. To calculate each significant digit there will have to be about 10 times as many trials as to calculate the preceding significant digit. Great Holiday Gifts!
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Eve Andersson (eve@eveandersson.com)
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Comments
Regarin the program
Hi eveander This is suresh here, doin my master in computers in ASU .As i'm a graduate student, actully we had a topic on monte carlo (pi
Home : Pi : One Calculation
________________________________________
The "Monte Carlo Method" is a method of solving problems using statistics. Given the probability, P, that an event will occur in certain conditions, a computer can be used to generate those conditions repeatedly. The number of times the event occurs divided by the number of times the conditions are generated should be approximately equal to P.
How this program works:
If a circle of radius R is inscribed inside a square with side length 2R, then the area of the circle will be pi*R^2 and the area of the square will be (2R)^2. So the ratio of the area of the circle to the area of the square will be pi/4.
This means that, if you pick N points at random inside the square, approximately N*pi/4 of those points should fall inside the circle.
This program picks points at random inside the square. It then checks to see if the point is inside the circle (it knows it's inside the circle if x^2 + y^2 < R^2, where x and y are the coordinates of the point and R is the radius of the circle). The program keeps track of how many points it's picked so far (N) and how many of those points fell inside the circle (M).
Pi is then approximated as follows:
4*M pi = --- N
Although the Monte Carlo Method is often useful for solving problems in physics and mathematics which cannot be solved by analytical means, it is a rather slow method of calculating pi. To calculate each significant digit there will have to be about 10 times as many trials as to calculate the preceding significant digit. Great Holiday Gifts!
________________________________________
Eve Andersson (eve@eveandersson.com)
________________________________________
Comments
Regarin the program
Hi eveander This is suresh here, doin my master in computers in ASU .As i'm a graduate student, actully we had a topic on monte carlo (pi