pi-monte-carlo: Estimate π using the Monte Carlo Method

Estimation of pi with a sample size of n=10000

Getting Started

Dependencies

• Cython is used for calculations to increase performance
• Random points are generated using Numpy
• Graphs are plotted using Matplotlib

Preperations

1. Clone the repository

git clone https://github.com/emrecil/pi-monte-carlo
cd pi-monte-carlo

2. Install requirements

pip install -r requirements.txt

3. Build Cython file

python setup.py build_ext --inplace

Usage

To start the program run the following command

python monte_carlo_pi.py

By default 10000 random points will be generated. You can specify a custom sample size as an argument:

python monte_carlo_pi.py [sample size]

How it works

First we draw a unit square which has an Area of . Then we draw a circle inside this square with a radius of 0.5. The area of this circle is .

Now we create n random points inside the square. With the ratio of the number of points inside the circle to the total number of points an approximation of π can be computed since:

and thus