@fabulousgrizzly np! 🙂

Wow, @RZ923, that's awesome! You are absolutely right. This is the closest next rational fraction that people can get.
We can also get a similar approximation using the following: \(\frac{04348}{33215}=3.141592654,\) \(\frac{208341} {66317}=3.141592653,\) or \(\frac{312689}{99532}=3.141592654.\)

Nevertheless, the number \(\frac{355}{113}\) is still very interesting. To read more about it, click here 🙂

🙂 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