Estimating the value of Pi using Monte Carlo method
Problem To estimate π using the Monte Carlo method, we’ll utilize the concept of randomly generating points within a square and determining how many fall inside a quarter circle. Monte Carlo Method Lets do the setup: Imagine a square with side length 2 centered at the origin, with coordinates ranging from (-1, -1) to (1, 1). Inside this square, there is a quarter circle of radius 1, also centered at the origin. The area of the square is 4 (since side length is 2), and the area of the quarter circle is (πr^2 / 4 = π/4) (since r=1). i.e. Let B be area of square, and A be area of circle $$ B = 4r^2 $$ ...