Sooner or later, almost every student comes across the most famous of mathematical theorems, the Pythagorean theorem. This theorem is encapsulated by the equation which states that a square is split additively into two squares. One may then ask for all triples of positive integers that satisfy this equation. We can uniquely parametrize all primitve Pythagorean triples using Euclid’s formula, and then scale them up to uniquely get all Pythagorean triples. We describe this parametrization in this video without proof.