🙂 This is a really cool shortcut!

Let's start with a radius of length 1 and increase to a radius of 2. The circumference goes from

2π(1) to 2π(2)

2π → 4π

The increase in circumference is 2π, and since π = 3.1415.... (Actually, go see the other Discussion on this lesson to see better approximations for π!), then 2π = 6.28.....

I like to use variables because they are more powerful tools. You can use them to generalize to all sorts of numbers.

Let's start from a radius of r, and go to a radius of (r + 1). The circumference changes from

2πr → 2π (r + 1)

2πr → 2πr + 2π

The difference in circumference is 2π = 6.28....

So it doesn't matter what value we use for r, the radius!

Happy Learning