This Python project provides an approximation of the mathematical constant π (Pi) using the Monte Carlo method. The approximation improves as more points are added, which is visualized through an animated GIF.
Monte Carlo methods are a class of algorithms that rely on repeated random sampling to obtain numerical results. In this case, we're approximating Pi by generating random points inside a square that encloses a quarter circle. By calculating the ratio of points that fall inside the quarter circle to the total number of points, we approximate the value of Pi.
- Monte Carlo Approximation: Efficiently approximates Pi by randomly sampling points.
- Animated Visualization: A generated GIF (
pi.gif) visually demonstrates how the precision of the Pi approximation improves as the number of points increases. - Adjustable Precision: Specify the number of decimal places of Pi that you want to approximate (up to 5).
To run the program, use the following command:
./draw.py image_size number_of_points number_of_decimals- image_size: The size of the square image in pixels (e.g., 500).
- number_of_points: The number of random points to generate for the approximation (e.g., 10000).
- number_of_decimals: The number of decimal places for Pi approximation (must be between 1 and 5).
$ ./draw.py 500 10000 3This will generate an approximation of Pi to 3 decimal places using 10,000 random points within a 500x500 image.
The project includes a GIF (pi.gif) which demonstrates how the Pi approximation converges with an increasing number of points. The precision improves as more points are added, showing the gradual refinement of the approximation.
Here's a preview of the generated visualization:
