Simon wanted to make an outside video this afternoon, about what he’s been thinking of a lot lately – continued fractions. In the video below, he looks for curious number patterns while writing irrational numbers Phi and square root of 2 as their continued fractions. Partially inspired by Mathologer’s videos.

Square root of 2 expressed as its continued fraction:

The Golden Ratio (Phi) and the Fibonacci numbers:

Phi expressed as its continued fraction: