https://github.com/giovanni-ottaviano/awesome-pi

A collection of peculiar ways to calculate PI
https://github.com/giovanni-ottaviano/awesome-pi

List: awesome-pi

cpp montecarlo montecarlo-methods pi python wynn-epsilon

Last synced: about 2 months ago
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A collection of peculiar ways to calculate PI

• Host: GitHub
• URL: https://github.com/giovanni-ottaviano/awesome-pi
• Owner: giovanni-ottaviano
• License: gpl-3.0
• Created: 2024-08-23T17:31:33.000Z (5 months ago)
• Default Branch: main
• Last Pushed: 2024-09-04T16:28:17.000Z (4 months ago)
• Last Synced: 2024-09-05T23:18:20.428Z (4 months ago)
• Topics: cpp, montecarlo, montecarlo-methods, pi, python, wynn-epsilon
• Language: Jupyter Notebook
• Homepage:
• Size: 455 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Awesome - $\pi$

![Alt text](images/spiral.png)

## 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](https://en.wikipedia.org/wiki/Irrational_number) and [transcendence](https://en.wikipedia.org/wiki/Transcendental_number).

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](https://en.wikipedia.org/wiki/Pi), [Wolfram](https://mathworld.wolfram.com/PiFormulas.html)