Summer of Math Exposition

The bit about double coverage at the end is interesting, and would be worth exploring why it’s like that (and the notion of “double cover” for topology or matrices in general).

This video is well produced but I fear it doesn’t add much to the understanding of how quaternions actually describe rotations intuitively. I see that there are formulas for this but this video seems more aimed at programming quaternions rather than understanding them. To be honest I haven’t seen another explanation for this but this video did not change my understanding of quaternions in any meaningful way so I’m giving it an “about the same”

I liked the idea of showing the actual Quaternion class from scratch to make it all seem less magical.

I really liked your test-driven development and how that naturally led to good exposition.

I know manim makes this hard, but the layering of the transparent sphere and the identical arrow tips made it hard to discern if vectors were pointing into or out of the screen at the start. But this got much better with your representation starting at 7:00.

I think you could say more about the exponentiation of quaternions you mention, or else how slerp makes sense.

Simple setup, easy on the eye visuals, clear narration.