Comment by ColinWright

One of the talks I give has this in it. The talk includes Continued Fractions and how they can be used to create approximations. That the way to find 355/113 as an excellent approximation to pi, and other similarly excellent approximations.

I also talk about the Continued Fraction algorithm for factorising integers, which is still one of the fastest methods for numbers in a certain range.

Continued Fractions also give what is, to me, one of the nicest proofs that sqrt(2) is irrational.