Estimating Pi with Random Numbers

Without any fancy formulas, it is possible to estimate Pi using random numbers.

We can use the Monte Carlo method to estimate Pi. The idea is to generate random X and Y coordinates and see how many of them fall inside the unit circle.

The probability of a point falling inside the unit circle is equal to the area of the circle divided by the area of the square. The area of the circle is Pi * r^2, and the area of the square is (2r)^2. So the probability is Pi/4.

After generating a bunch of random points, we can estimate Pi by dividing the number of points that fall inside the circle by the total number of points multiplied by 4.

Here’s a demonstration of the Monte Carlo method in action:

See, eventually, the points will start to form a circle. The more points you generate, the more accurate the estimate of Pi will be.