Summer of Math Exposition

Solid video. Clean animations, good, clear explanations, and answers a question that not many in high school learning about this topic might think about. Overall, good job!

Nice explanation of the formula. I think if you also animated the calculations of the example problem, it would be even better and you could aviod something like that the answer is squeezed into the corner at the end.

The derivation is good and pretty. The example is helpful, but it gets a bit bogged down in details. The big thing that’s missing for me is motivation. Why is arc length something we want to compute at all?

It’s a nice and clear explanation of this concept with good visuals. You provide a nice general treatment and then you work on an example which is also nice. Although I think the example takes quite a lot of time (more than half of the video) and why did you decide to do it in handwritten (or mouse-written) form? I think it would be much more clean and clear if you animated it like the rest and people can pause and work on the example themselves in parallel if they cannot follow along. Your voice also sounds a bit monotonous and not so engaging. But all in all it’s a decent explainer.

The video is split into two parts, the theory and the example. The theory section is done very well, the diagrams are placed in the correct positions and it looks great. One suggestion is to use a colour other than white for the slopes because it is a bit hard to see, the other colours are fine. The example section can be improved by writing on straight lines. One of the appeals of Tex objects is how nice the font is, so to match the quality you should also try using a better writing tool. You can write very nice equations using chalk+blackboard, marker+whiteboard or stylus + tablet, the method you used looks similar to paint which is a bit harder to get right.

Overall, you gave a good explanation and examples were good. Presentation can be improved slightly.

This video is good, but has a very traditional approach. It would have been nice to have a non-abstract motivation, an actual problem, at the start. This could also have been reused as the final demonstration. I think your actual derivation could have been a bit faster from the point where you refreshed the standard integral onwards. I skipped the demonstration problem since it didn’t interest me and rate as if it hadn’t been there. All in all, this is a good video, just “about the same” as what’s already available.

You should take a little bit more care to distinguish between functions $\mathbb{R}\to\mathbb{R}$ and curves $\mathbb{R}\to\mathbb{R}^2$. That’s a common sticking point. But apart from that, a really nice explanation!

In the back half of the video, did you do the handwritten stuff with your mouse? If yes, it’s surprisingly legible! But you should think about getting a small graphics tablet (or even a tablet).

First half was great, second half felt a lot slower