Monte Carlo Pi Estimator with Visualisation

This Python script estimates the value of π (pi) using a simple and intuitive Monte Carlo simulation, now enhanced with a matplotlib visualisation.

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Idea Behind It

We randomly generate points inside a unit square (1×1) and count how many fall inside the quarter-circle inscribed in that square.
Using this ratio, we estimate π based on the formula:

π ≈ 4 × (points_in_circle / total_points)

This method is inspired by probability and geometry – and now also visualised!

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▶How to Run

python estimate_pi.py

You will be prompted to enter a number n, which defines how many random points the simulation will use.

Example:

n = 10000
Pi ≈ 3.14124

A scatter plot will show:

• Green dots = points inside the quarter circle
• Red dots = points outside the circle
• 

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Requirements

• Python 3.x
• matplotlib (install with pip install matplotlib)

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File Overview

File	Description
estimate_pi.py	Main script that performs the simulation and plot
README.md	This documentation 📖

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Author

Sebastian Strack
2025
Feel free to fork, modify, or visualise more!

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Optional Ideas

• Animate the points being drawn
• Track π convergence as number of points increases
• Compare multiple simulations