This starts with some bonus patreon footage I deliberately filmed. You can see it exactly flows off a shot from the main video (although I later had to extend the pause in the main video when I decided afterward to add a "total ellipse of the chart" there). This is me talking about why my approximations are so different for ellipses which are very close to being circles.
And then there is a deleted scene which was going to be in the main video but I decided to take it out at the last minute. It talks about how for extreme ellipses the perimeter approaches 4a. My lazy approximation approaches (5π/6)a which means there is an upper bound on the percentage error.
Main video is here: https://youtu.be/5nW3nJhBHL0