Awesome - $\pi$

Overview

$\pi$ is probably the best-known mathematical constant in the world, so famous that it even has a dedicated day (March 14th). It's defined as the ratio between a circumference and its diameter and two of its most remarkable properties are irrationality and transcendence. Although we are used to thinking of it in relation with circles and angles, it can be found in many different fields and applications; showing some not-so-usual formulas in which you can find $\pi$ (and calculating its digits) is precisely the purpose of this project!

For now, the implemented methods are as follows:

• Monte Carlo: Circle method ($C++$)
• Monthe Carlo: Buffon's needle ($C++$)
• Function integration ($C++$)
• Leibniz series ($Python$)

A comparison of the results can be found in the Jupyter Notebook.

Usage

The src folder contains a different sub-folder for each method and a Makefile for compiling every given program in $C++$.
Every sub-folder contains a README file with a quick overview on the method and the specification for the algorithm, such as input parameters to customize the execution.

The folder results contains the results after an example run for every method.

Contribution

Feel free to fork this project and test your own configuration. You can also pinpoint errata or new techniques that should be implemented.
Any feedback is welcome!

References

Some useful resources: Wikipedia, Wolfram