Summer of Math Exposition

I find that connecting maths to art is very valuable, especially for students who don’t find such joy in maths.

Upvoted for cat. (Also for good mathematics, but… cat.)

A little too brief, it doesn’t feel like we’re ever “with” the topic at hand before it ends. Nice structure and presentation style, though.

A bit simple but pretty fun. It would have been cool to go a bit deeper into the subject

Super entertaining and succinct. The right amount of detail to get someone excited without bogging down the video. Would like to see more exploring creating art with sine waves. What art can you create with Fourier analysis?

Fun video. But it glides over several concepts which required a deeper dive and intuition. For example, around 2:00, the video mentions we can add sine waves to get a complicated sine wave. But how are we adding them? Are they different or same sine waves? If different, what ways are they different?

Video could use narrowing down on the topics and diving deeper into them a bit more.

I was not expecting the link to animation, which was nice, but could use more examples. For instance, the grass that was supposed to be better animated looked basically similar to the crude sine version of the animation.

The decomposition of such „daily” sounds as a cat screaming into sine waves and then, importantly, putting them back together starting from fewer modes, is something I haven’t seen much and it was great! It really makes you intuitively believe in the Fourier transform. And so, more examples of that would be very welcome.

Overall the idea is cool and the specific examples fresh - but they could just use more exposition, more time to sink in :)

This is a good video, but I don’t think it stands out. Starting with a nitpick, I don’t think your anecdote in the intro leads anywhere and thus doesn’t help with motivation. When you went into the parameters of sine, I think it would have made sense to not just change the parameters on screen, but also do a before-after comparison in some cases, e.g. showing what a doubled frequency looks like in direct comparison. I don’t have much to say about the 1D and 2D applications. They are nice, but often seen. I liked how when you showed different resolutions of the meow, the video footage’s quality was also scaled; a nice touch. In conclusion, the video felt like a casual display and did that well, but doesn’t stand out. I wouldn’t be surprised if teachers see that differently since I see you targeted that angle.

The quality of the video is really high, but content-wise I didn’t learn anything novel or surprising. The explanations are very surface level. I very much liked the Fourier decomposed cat sounds:)

By no accident, this video’s treatment of its subject is surface-level. It aspires to give its target audience only a glimpse of what is to come, and it excels. What stood out to me was the video’s deliberate decision not to go in-depth into how sine waves are defined or what distinguishes them from similar-looking waves. I will keep the target audience in mind when judging this video. In fact, I would consider the video’s audience tags of high school and above ill-fitting, considering that it seems to be for students who haven’t even learned trigonometry yet.

The introductory motivation accomplishes its purpose. First, there’s a personal anecdote to emphasize with newcomers. That transitions into a list of places where trigonometry is useful, which plants the seeds for why people care about the topic, even if the topics are too advanced to be elaborated on in this video. For now, the intro ends by getting to the main subject of the video: doing art with sine. Since art is something that people largely admire, I’m sure that many of them would find this subject inherently interesting.

There are positives and negatives to the video’s clarity. Keeping in mind the target audience, the video sticks to simple words while still communicating properly. The approach to jargon is instructional: the video introduces and demonstrates a concept, then it uses that to teach the relevant term to the viewer.

However, a few visualizations are rushed through when they don’t need to be. At 1:55, the video demonstrates the sum of two sine waves. This demonstration could be improved by actually showing each sine wave individually, as well as what it visually looks like to add their values. As another example, the concept of a graph of a two-variable scalar-valued function is brought in at 2:54, one which many in the audience will likely be unfamiliar with. Even an additional 30 seconds or so to to explain the concept would probably have gotten viewers more comfortable with it.

The last main point that the video covers is the fact that adding sine waves gives you sound. Of course, again, this is not covered in much depth, and the video outright tells you to go to other sources if you actually want to know how it works. At least the idea is conveyed clearly, if not the mechanics.

This video definitely takes a novel approach. I’ve never seen someone so much as acknowledge the existence of Fourier analysis to an audience that can’t define what a sine wave is. I would say that the video has value in that regard, in that it uniquely aims more so to spark interest in the topic than to actually get the audience to understand it. Now, will the material covered in this video stick with the viewer, particularly until they actually learn the topics in more depth? Unfortunately, I can’t exactly speak on their behalf. It’ll vary from person to person, but as long as it sparks the curiosity of some young learners, it’ll be worth it. To sum up, even if the video is relatively light, I can appreciate its merits as a mathematical taste test. I will give a score of 6.00.

Minor notes:

2:07 g(x) = sin(f_1 x + p_1) + sin(f_2 x + p_2) is not necessarily periodic. The sum of two continuous periodic functions is periodic if and only if their periods are commensurable, i.e., if the ratio of the periods is a rational number. We can choose f_1 and f_2 to be whatever real number we want, so f_1 / f_2 can be either rational or irrational.