Summer of Math Exposition

It would be nice to have context for why we care about orbits and what the key takeaways are for finding the iterative square root.

Really interesting to see the idea of orbits used and how their independence in this problem relates to degrees of freedom in finding “iterative square roots”. But I found the descriptions quite dry and hard to follow especially around minute 9-10 or so when many of the images where just bullet points of equations including things like “Ord[a]” that I wasn’t even exactly sure what that meant.

I was missing some motivation for this problem. I wasn’t keenly interested in knowing the answer from the hook, which made it harder to pay full attention when the details got difficult.

What is missing: why do we want to look at iterated functions, or the “functional square root”?

I really like the starting problem and I think you did a great job at motivating the math shown throughout the video. The first half of the video was a little slow, and the second half was a little fast. I would’ve liked each of the definitions to be more thoroughly explained, but the video was still an interesting watch.

The motivation is neat and I haven’t seen this topic before so I’ll give it novelty too, but the clarity and memorability are lower. You’ve chosen to come down heavily on the side of rigor and formalism, for a topic that I think would be much better presented in a more intuitive way. You arrow graphics are a good step in this direction, but dwelling too long on the formal definitions of orbits and the exact details of the functional notation detract from this. You also did not really show the answer to one of the early questions meant to generate interest (you showed the graph but not a functional form or how to derive that graph otherwise).