🙂 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!