Monte Carlo methods, or simulations, are a broad class of computational
algorithms that rely on repeated random sampling to obtain numerical results.
One method to estimate the value of π (3.141592…) is by using a Monte Carlo method.
This methods consists of drawing a square with an inner circle. Then
counting how many fall in the enclosed circle.
The area of the circle is 𝐴 = 𝜋𝑟2
The area of the square is 𝐴 = 𝑙𝑒𝑛𝑔𝑡h2 = (2𝑟)2
If we divide the area of the circle, by the area of the square we get π/4.
The same ratio can be used between the number of points within the square and
the circle
Hence we can use the following formula to estimate Pi:
π ≈ 4 x (number of points in the circle / total number of points)
| Pi History | ||
|---|---|---|
| # | Pi | Number of Points |