Implementing Monte Carlo integration to calculate an approximation of π
π is a mathematical constant, representing the ratio of a circle’s circumference to its diameter. It is an irrational number, and as such has a never ending decimal approximation. Approximating π was once done geometrically until methods involving infinite series were introduced. More recently, however, computational methods have been introduced that take advantage of ever improving processing power.
One such method, Monte Carlo integration, is an interesting numerical technique for solving integrals using a hit or miss approach. To approximate π, a circle of a certain diameter and a box with dimensions that match the diameter are considered. A number of random coordinates pass through a conditional statement. If the random coordinate falls within the circle based on a right handed rectangular Cartesian coordinate system. then one is added to the total of successes. In the end, this number of successes is compared to the total number of random coordinates. The result should yield an approximation of π.
Clone this repository
git clone git@github.com:jpweiser/MontePithon.git
Change to program directory
cd MontePithon
Requirements: Python 2.x
From terminal:
cd bin
./monte-pithon
usage: main.py [-h] [-i ITERATIONS] [-r RADIUS] [-p] [-v]
Use Monte Carlo integration to approximate PI.
optional arguments:
-h, --help show this help message and exit
-i ITERATIONS, --iterations ITERATIONS
Number of iterations to use for approximation
-r RADIUS, --radius RADIUS
Radius of circle to use for integration
-p, --plot Plot result
-v, --verbose Toggle verbose output