Gauss–Legendre algorithm

The Gauss–Legendre algorithm is a method for calculating the value of pi with high precision. It works by starting with simple numbers and repeatedly updating them using specific formulas. Each iteration gets the numbers closer to pi, rapidly increasing accuracy. It uses concepts from mathematics called arithmetic and geometric means. The process converges quickly, meaning it needs fewer steps to reach very accurate results. This method is especially efficient for computing pi in computer algorithms, making it a powerful tool in numerical calculations and scientific computing.