Approximating pi Using the Monte Carlo Method

Approximating mathematical constants such as $\pi$ is one of the classical challenges in computational science and numerical analysis. This project presents a geometric Monte Carlo simulation to estimate $\pi$ using uniform random point distributions in Python. The implementation evaluates spatial enclosure, calculates standard probabilistic errors ($1\sigma$ and $3\sigma$), and analyzes asymptotic convergence ($1/\sqrt{N}$) through cumulative estimation routines.