Approximating Pi Using the Leibniz Series in Python

Leibniz series is a classic method for calculating pi, and its formula is as follows:

π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...

This formula approximates the value of π by continuously accumulating finite terms;

Sample code

The following is a Python sample code that uses the Leibniz formula to calculate pi:

def estimate_pi(num_terms):
    pi_estimate = 0.0
    sign = 1
    for i in range(num_terms):
        term = 1.0 / (2 * i + 1)
        pi_estimate += sign * term
        sign *= -1
    
    return 4.0 * pi_estimate

# 调用函数进行估算，num_terms为级数项数
print(estimate_pi(1000000))

By adjusting the value of num_terms, we can improve the accuracy of our approximation of pi; although the Leibniz series converges slowly, it provides a simple and intuitive way to calculate π.