Sequence article

Unlike squares or rectangles, circles don't have any straight sides. If you draw a circle on graph paper, you'll find that it's hard to get an exact measurement - there are a lot of grid squares that are partly inside the circle, and partly outside. It's not clear how to count them.

Instead, let's start by estimating the area of the circle first. Since calculating the area of a square is easy, we can estimate the area of a circle by comparing it to squares that are smaller and larger than it.

The area of the square on the left is $7^2=49$‍ and the area of the square on the right is ${10}^2=100$‍, so we know that the area of the circle must be between 49 and 100. That narrows it down a bit, but we still don't know exactly what the area is. How can we find out?

Let's try cutting up a circle to see if we can rearrange it into a more familiar shape. Look below - see how the four quarters of a circle can be fitted together? The slider controls how many sections we divide the circle into. Slide it to the right to see what happens when we increase that number!