Summer of Math Exposition

Best animations from any math channel I’ve seen. And explained pretty nicely too!

Beautiful video. A joy to watch.

The topic was unique, visuals were captivating, and I came away from it learning something new.

The only thing which could have improved it for me is that sometimes I felt the mathematical explanations were a bit quick - I would have liked to have seen more on the theorems or proofs about toroidal knots (and connection to the Fibonacci sequence).

Thank you for the great submission! It really showcased how beautiful maths is!

These are really beautiful animations!

Your connection with concert pitches seems to be looking too far into numerical coincidences though. You rounded the golden angle (137.507764… degrees) to one decimal place and then noticed consequences of having rounded it to one decimal place: you took 55/144 of the circle, and then saw the number 440 because it’s a multiple of 55. You saw 432 because it’s a multiple of 144. There is nothing natural or fundamental about the numbers 432 and 440 nor even the duration of one second used to define hertz. These are accidents of human history.

Regardless, this seems like a fun way of visualizing some sounds.

Throughout the video, the degree is used as the unit of angle measurement. However, the turn seems to be a more natural choice in this context. Using the degree only seems to introduce an unnecessary factor of 360.

The process of arriving at the golden torus knot is dubious. The winding interval of a torus knot can only ever be a rational number of turns, so the golden torus knot could only be produced by a rational approximation of the golden ratio. Initially, the video seems to just ignore the fact that it’s an approximation (timestamp 3:18), which feels misleading. The video goes on to justify that 55 / 144 is the first ratio of an nth Fibonacci number to the (n + 2)th Fibonacci number which resembles 1 / (golden ratio)^2 “very closely” (timestamp 6:28), which seems like a hand wave. By the way, the video confusingly uses the letter phi twice to denote two separate values related to the golden ratio rather than to denote the golden ratio itself, which is a strange choice of notation.

At 5:14, four images are shown of things that supposedly relate to the golden ratio. In every one of these four cases, the idea that this relation exists is a common misconception. To be fair, none of these things are made significant anywhere else in the video, but the propagation of mathematical misconceptions is still a problem.

The connection to music was made by noting the choices of frequency for the golden torus knot that resulted in clear patterns and realizing that they aligned with the number of Hz in notes of our typical musical system. I was not compelled to believe that this was more than a coincidence. What if we had, let, say 435 Hz be the standard concert pitch? The choice ultimately seems arbitrary.

The pattern formed by each frequency is easily distinguishable between different temperament systems, but it’s unclear whether the patterns within a temperament system in isolation say anything meaningful. The video seems to say so, but it doesn’t go too deeply into the topic. At least the patterns are pretty, though.

Overall, I did learn a few interesting things from this video, and the visual presentation is good, but it’s not a standout. My rating is 5.00.

Awesome way of visualising musical frequencies.

In the beginning I missed a motivation behind defining these knots in all the different ways.

Also, does the 55 144 knot really resemble the golden ratio? To my understanding this seems more like a rounding thing. If I am wrong, I would have liked a mini-explainer on why exactly those numbers and not some further down the Fibonacci sequence.

In general, I would have liked more of an explorarion of why all these numbers (primarily 440 and 432) show up instead of just noting it.

This video has stunning animations, I really like the style. Also this video definetely piqued my curiosity.

It looked really cool. Lord knows I didn’t get most of it. Felt like a lot, and I was really only interested in the middle part about music, but didn’t feel like a learned much either.

It is difficult for me to rate this one : if I understand well (and I am not sure of that, my comment is to be taken with care) this (very beautiful and spectacular) video mixes some rigorous things, and some others which are far from actual science.

(I put 5, but this could be 2 or 9 depending on I am right or wrong.)

For example, the fact that the standard A at 440Hz gives nice patterns seems to me as a pure coïncidence. It has nothing to do with the golden “powerful” ratio”… It is like playing with Lissajous curves on a oscilloscope.

I suppose that this will be challenged also (or better understood :-) by some other voters. But at this stage I would be very cautious to show this as a scientific video.

On another side, the video is absolutely bluffing in terms of “show”, and also in terms of what can be done by coding and exploring parameters family. This aspect is absolutely brilliant and could be a strong inducement for students to learn coding.

This is a very nice video with an interesting topic and fantastic visualizations! The explanations are also great and well structured. There aren’t many negative things for me to point out here, great job!

Astounding visuals. I enjoyed the application of knots to music theory. I wonder how easy would be to make an app that would use this method to visualize sound captured by mic. I also wonder why the numbers for defining a knot need to be relatively prime, perhaps there’s some interesting math behind that. And also why certain patterns appear. Can we predict when and what type of patterns would appear? Very amusing video!

Very good, it’s a topic I’ve never thought about before but it was clearly explained and I thought the ways in which the torus was animated and used (i.e. making the winding angle the golden angle, noticing various patterns in different frequencies, and then using the changes in these patterns as visual indicators to illustrate the slight differences between various tuning systems)

I didn’t appreciate the The Golden Ratio Is Everywhere! claims relating to things like the Parthenon, however

These are the best looking animations I’ve seen so far. I’m wondering if the three values mentioned at the end are related to the three pyramids at Giza since they’re in the same configuration