A student recently shared the following: https://www.youtube.com/watch?v=yk6wbvNPZW0&feature=youtu.be

This includes some work I did with a student, David Montague, a few years back in SMALL. The animation is terrific; my favorite example is our proof of the irrationality of sqrt(5) (starts at 9 minutes). The paper is here: Rational irrational proofs (with David Montague), Mathematics Magazine (85 (2012), no. 2, 110–114). Expanded version: https://web.williams.edu/Mathematics/sjmiller/public_html/math/papers/irrationality50.pdf

The inspiration for this work was a great senior colloquium given by Margaret Tucker, advised by Ed Burger, on six different proofs of the irrationality of sqrt(2). Frank Morgan commented to me that it was a wonderful talk, and wondered if one of the proofs (the geometric irrationality proof by Stanley Tennenbaum) could be extended to other numbers.

There are many related questions one can consider; if interested email [email protected].