Summer of Math Exposition

Impressed by the double factorial definition. Impressed by the art style. Impressed by your limits.

Very well done. Gets to the point very quickly, and the concept it easily and elegantly explained

The explanation was generally clear but not really engaging. There was creativity in introducing the W_n integrals to get to the solution, but it was treated similarly to how a math professors might approach explanation of a proof. As in, “this is where we need to go and this is how we got there,” but there wasn’t much describing why it would be interesting.

I liked the visuals of this video a lot! Clean, interesting, yet minimal. Following the explanation is easy, the algebraic manipulations and tools which are used, are animated nicely. I’m not sure what was meant around 5:00 with saying that n will be equal to n+1 or W_n being equal to W_n+1, perhaps the role of limits here should be explained a bit differently. Just stating that limits “contradict our line of thinking” doesn’t feel enough. Otherwise, nice to watch, interesting and not too long.

Unfortunately, the music is too loud. It almost overpowers your voice, which makes it difficult to concentrate on what you’re saying.

This video seems deceptively simple and the animations aren’t the best I’ve ever seen, but it works very well as simple as it is.

It’s not a branch of math that I perfectly understand (yet), but I understand the value of this video after watching it. The explanation is clear; your motivation is of course a little random but I got intrigued nonetheless; novelty-wise it’s new to me but it doesn’t have the wow-factor that makes a video memorable.

All in all one of the better, although also simpler, videos that I’ve seen. Keep it up! With this being your first video, you have a bright future ahead!

It’s a bit weird that you talk about limits like if the viewer didn’t know how they work considering you talk about integrals before in the video.

The animation was a little distracting, but the proof was clearly explained.

The framing of scrolling wikipedia is enticing and normalizes curiosity. The style matches the rigor of the math being done. I think the video was a good length b/c we don’t need to connect it to the real world: it’s just a neat trick.

The intro was great and really sparked my curiosity.

I like how you animated the equations, but when the equations got longer/more complicated it was a bit distracting.

Spots where the video is plain black: opportunities to put an interesting visual

This would be great to show to calculus students, however a bit hard to follow as the video got more complicated in the end.

Keep making videos!

This topic is certainly interesting and appealing for mathematicians, but it is not within the reach of high-school students. These students would not be generally interested, and the chosen approach does not seem very original or engaging: it is too technical.

Insightful investigation! Well structured and argued. Also, very cool graphics and nice language (and music). One thing the video could explore is whether $W_n$ over $W_{n+1}$ would actually converge to 1 for big $n$ because if not, then $W_n \sim W_{n+1}$ wouldn’t be super sound; it’s not something people can just decree. This is justifiable, luckily, via convergence tests and graphing of your choice. Other than that, a really fine first effort — well done.

This was neat, but I think there were a few memes and jokes that got in the way of the math. This was especially the case in the limits section.

Thank you very much for contribution and the very nice animations! It is a very focused video on an interesting question.

Here are few comments from the point of view of SoME4:

1. A tiny one at the start: although I very much like the music from Erik Satie, I advise turning it down a little bit, so that your voice comes out a bit better!
2. When you write down the formula for the double factorial, your notation is prone to misinterpretation: multiplication has precedence over addition, so that your formula, strictly speaking, is nonsensical. For future work, I recommend putting parentheses to clarify the meaning. Also note that a product symbol with a fraction as a limit is not reaaalllyy well-defined…
3. Similarly to the previous point, the caption $\cdot 1\text{ or }\frac{\pi}{2}$ is very confusing. I did not understand the meaning until you explained it. Instead, it would be easier to understand if you were to write $\cdot \Big( 1 \text{ or }\frac{\pi}{2}\Big)$.

I think the general takeaway is that you could be a bit more careful with the math that you write down (without actually making the math harder). Continue the good work!

For me, this was a nice explanation of an equation I feel I’ve seen before but hadn’t stopped to think about. I definitely was surprised when the Wallis integral showed up. That said, I don’t think I am (read: should be) your target audience, which I think is at the undergrad level. Because of that, I think the video would have benefited from stopping to smell the roses a little with the computations.

For somewhat subtle reasons, I don’t feel this is appropriate at the high school level. I’m not bothered that much by the use of calculus (as you mention, it’s only used a little and I’m fine to say calc is a high school topic), nor the pi notation (although a brief bit of explanation would have been nice; it’s not standard in the US at least). The first place that really got to me was the transition from the recursive formula for W_n to the closed form expression. Armed with a full slate of high school math classes, the viewer certainly could understand this conversion, but even then it would be polite to linger on it for a moment, maybe unpacking it with an example. In principle, the “ease” on the creator’s end of doing that unpacking semi-formally is one of the main advantages a viewer expects of animated video instead of writing on paper. (Upon looking back, I also think the video as a whole fairly under-motivated, and the high school audience is going to be more sensitive to that.)

The music was a good idea but I think detracted a bit at times. I’m not sure how I feel about the wiggling equations. Experiment with that.