Drilling a Square Hole

Have you ever considered how to make a hole in any shape other than a square? The geometry of this is very challenging, and somewhat counter-intuitive. Does anyone remember Spirograph?

The solution is like something you'd find in a box of spirograph tracing tools. I found this excellent video, which is apparently in russian, which does an amazing job of teaching you how this triangular-ish type shape, when rotated, actually traces out a square perfectly and shows you how to indeed, drill a square hole.



I love science. I love geometry. Does this not impress you?