Monte Carlo simulation to approximate the value of pi
Given a unit circle (r=1) inscribed inside a square of side length 2, we can calculate the areas of each shape as follows:
A_square = (2r)^2 = 4 A_circle = pi(r)^2 = pi
Using a Monte Carlo simulation, we can then assess how many random points land within the circle compared to how many points land outside of the circle.
Proportion of points inside circle = A_circle/A_square = pi/4.
Therefore, we approximate pi as 4 x proportion.