I've always found the approximation of a circle to the limit as n -> inf of a polygon of n equal sides to be interesting. I do have a question though: is it possible to extend this method of exploration to reconcile the irrational property of pi? Because I'm somewhat discomforted with being satisfied with approximating our "best pi" to 3.14.

Think of irrationality as a form of infinite precision, such that no matter how many numbers you write down it’s always an approximation because there is always a more precise form. Now think of the number of sides as increasing your precision. Meaning there is an n such that every approximation after will read 3.14… and another for 3.141….