This video, The Tale of Three Triangles, is a long form video discussing the convergent behavior of the random Chaos Game, the deterministic Sierpinski’s triangle, and the combinatorial Pascal’s triangle. This video took me months, over 5000 lines of animation code, and a script longer than any of my philosophy essays. It was eventually recognized by 3Blue1Brown as an honorable mention for storytelling in the Summer of Math Exposition #1.
This video, one of the first that I made, demonstrates the closed-form expression for the Catalan numbers using a reflection proof.
Ramsey Theory studies the existence of substructures in graph theory. In this video, one of the first I made, I show that the Ramsey number R(3,3) is 6.