Imagine a quadrant of a circle is placed inside a square, as shown next, and we generate some random points inside the square. You can see that some of the points fall inside the circle while others are outside the circle:

We can write:

We know that the area of a circle is *πr ^{2}* and the area of a square is

*a*:

^{2}Let's consider that the radius of a circle is one half and the square's side is *1*, so we can ...