Summer of Math Exposition

It's nice little trick, but I've seen something very similar done, and also some different transformations of 2D planes to fit them into limited area. I miss why this is actually useful, I'd like to see some example functions where by looking at their graph in this form we gain some useful insight.

The only problem I noticed is the quality at the start of the video.

This video is short and to-the-point. The problem of visualizing graphs in a helpful and meaningful way is no doubt one that will be relatable for many people looking for math content on youtube, and you provide a quick and clever idea. Your visualization of how you do the projection is very nice, I like that it feels very hands-on in a way that sometimes a video with beautiful but uninteractive graphics is not. You even link to a couple nice Desmos files for people to mess around with, which is awesome. On the other hand, because your video is so short, and so narrowly interested in providing an answer to the question "how can you view an entire function at once", it felt like it lacked substance. I don't think I learned enough in this video that I'm going to remember it in a couple months. One area that I think you could have elaborated on is when you point out that the square root function appears to approach y=0 as x goes to infinity. That's a really interesting thing to point out, I think you could have talked more about why that is. Some further questions this raises to me are: given a function, is there a way for us to tell which points that function will "appear to approach" when graphed this way? How is this related to other instances of things "appearing to approach" certain points that we know they can't actually reach, like how train tracks look like they meet at the horizon? These ideas are important to perspective in art, as well as to the mathematical area of projective geometry, and I think making that connection would have given your video a lot more impact and memorability. Another thing I think would help would be to refer to other math videos on youtube that cover similar things, and discuss how your presentation relates to theirs. The trick you use is essentially stereographic projection, which is a topic that has received a lot of coverage in other math youtube videos. On a quick search, I found videos by Henry Segerman, 3B1B, and Michael Penn, certainly three big names in youtube math videos. Given this, I found it odd that you don't actually mention by name that the trick you're using is related to stereographic projection. I think it would have made the video better if you had pointed out that there are other resources on stereographic projection already on youtube, partially because then people who are interested in your video know where they can go to learn more, and partially to highlight that using stereographic projection specifically to "view an entire function at once" is something distinctive to your video.

Somewhat unique concept and the video is nice and concise and well-made. However, it doesn't feel particularly well-motivated. Is this technique used for any sort of analysis? Does it have ties to any other fields of math? Why would I want to do this, other than the vague idea of "see a whole function"?

Small topic but gave me a new way to visualize things

Nice idea ! A suggestion : explain with more details how "zooming" is performed (I suppose it corresponds to an increase of the radius of the projection hemisphere, but I am not quite sure)

Great video on a topic that I think is unknown to most people. The visualisation and the "animations" are very clear. The only change I would do if I could, is to show explicitely in the video the equations that describe the change of coordinates, even if they can be found in the Desmos file or derived analitycally.

Pretty!

I really like the idea and how you explain how you came up with the projection. Once I got the idea the video was a bit long though, but I guess it depends on the audience

Interesting way to make a complicated thing look a lot more simple. Scores well for everything

Accessible explanation, and I like that you make it interactive by linking to the Desmos file. Would have liked to see at least a mention of what this projection is called, so people can google it to learn more

where is the explantion of program ?

Neat example!

surprising topic I learned a new idea in a very efficient and quick way. clear pronounciation and language The graphics look easy to create, but they are very useful. It's a very short video, but perhaps that's no hindrance here.