How to Write a Python Program to Calculate Pi

Introduction

Calculating the value of Pi is a classic problem that has fascinated mathematicians for centuries. In this article, we will explore how you can write a Python program to approximate the value of Pi using various techniques.

Using the Monte Carlo Method

The Monte Carlo method is a popular way to estimate Pi by generating random numbers within a square and determining the ratio of points that fall within a quarter circle inscribed in the square. Here is a simple Python program that demonstrates this technique:

import random

def calculate_pi(n):
    inside_circle = 0
    for _ in range(n):
        x = random.random()
        y = random.random()
        if x**2 + y**2 <= 1:
            inside_circle += 1
    return 4 * inside_circle / n

n = 100000
approx_pi = calculate_pi(n)
print(approx_pi)

This program will generate n random points and approximate Pi based on the ratio of points inside the quarter circle to the total number of points.

Using the Nilakantha Series

Another approach to calculate Pi is by using mathematical series such as the Nilakantha series. This series converges to Pi and can be implemented in Python as follows:

def calculate_pi_nilakantha(iterations):
    pi = 3.0
    sign = -1
    for i in range(2, 2 * iterations, 2):
        pi += sign * 4.0 / (i * (i + 1) * (i + 2))
        sign *= -1
    return pi

iterations = 1000
approx_pi = calculate_pi_nilakantha(iterations)
print(approx_pi)

By running this program, you can obtain an approximation of Pi using the Nilakantha series with a specified number of iterations.

Conclusion

Writing a Python program to calculate Pi can be a fun and educational exercise. Whether you choose to use the Monte Carlo method, mathematical series, or other techniques, exploring different approaches to approximating Pi can deepen your understanding of both mathematics and programming.