Summer of Math Exposition

Sorry dude but it’s very hard to process hand-drawn diagrams.

Hey, thanks for participating this year! I think you’re onto something with your choice of topic here, because this sort of identity is something that many students just memorize, often without ever seeing the proof for why it’s true, despite the proof being entirely possible with their skillset. I agree this is an issue - in fact, I actually also made a video on this topic in preparation for my entry. (zero obligation here but in case you’re interested - https://youtu.be/LTG6ZmNrpzk)

In particular, I made that first video in order to practice my Manim, which I think was very helpful to me in terms of managing the details in that diagram and showing how they arrive into the identities, and I think doing this slightly more traditional presentation, you struggled a bit with the diagram getting busy and hard to read, especially with the quick pace of the video. I’m not trying to push Manim onto you, if doing things on paper makes things much easier for you, but if you go with this method, I think having multiple copies of your diagram, traced or printed onto multiple pieces of paper, might help so that details can go away once they’re no longer needed. (I also think using something like a ring cutter to get a neater circle, or just doing away with the circle altogether since it only gives us our radius of 1, could neaten up the presentation a little)

This part might be hypocritical of me because my video on this topic has no voiceover, but I think if you are going to talk through the proof, people tend to absorb the content better if the communication is slightly more naturalistic - imagine more like you’re describing the logic behind the proof to your friend, you would probably have more full sentences and less just tags for what each step literally is. (This could also just be a stylistic choice for “Trig ASMR” - in which case, no complaints, just wanted to say something about how mathematical writing tends to have more “writing” than people expect.)

I want to be clear, I’m very glad that you made this video, and I think it’s a great first step in learning how to do these sorts of presentations and finding your personal voice. I know my feedback has been critical, but I hope it’s clear that the intent is only to help you improve, and I would love to see you do more in the future.

Have a nice rest of your day!

This gives me big “AndyMath” vibes. I often enjoy videos that take a deceptively simple problem and break it down step by step, and this fits right into that niche. I like your adaptability in creating your video using pen and paper slides. I might have suggested giving the drawings one more attempt for better readability.