What is the most motivating way to introduct Pythagorean triples to undergraduate students? I am looking for an approach that will have an impact. Good interesting or real life examples will help. Is there any resources for this?
I saw this video a long time ago, I thought it was interesting. The talk is aimed to be a talk about one of the Millenium Problems but aimed at a general audience (so undergrads should understand/follow it). It is the first a in series about connecting Congruent Number Problem to the BSD Conjecture, and the 2nd video in the series describes the idea of generating Pythagorean Triples to help find Congruent Numbers.
This video Might be a bit elementary for Undergrad, but it demonstrates a way to program Excel to find Pythagorean Triples for you by using Brute Force. The follow up video shows the algebraic manipulations to generate all the primitive triples.