Summer of Math Exposition

It was enlightening but I thought the audio was lacking. I would have liked some more enthusiasm in the voice and maybe a little bit of going back and forth. Sometimes in the video I felt lost and wanted to scroll back.

The use of areas to create this visual proof was something I hadn’t seen before.

The proof was nice, but since this is a video, the sound effects really affect its enjoyment. I wouldn’t say the problem is that they are too loud, but that they are louder than the author’s voice by comparison, which makes changing volume annoying.

I feel like the motivation for the video wasn’t very strong. change in audio quality wasn’t good. i liked the little sound effects, made it feel ‘alive’. great visuals, and it was easy to follow the explanation.

The visualization makes the proof easy to follow. But the proof relies on some clever constructions. I’d like to see how someone might have come up with it.

Nice video, showing a visual way to understand different averages. I find this to be quite novel when explaining them. Few suggestions to improve clarity: I feel the pacing is a bit fast at times, even in the beginning when the numbers move all the time before I get a chance to read them. The sound effects are a bit much, sometimes making it hard to understand the voice if they overlap. Memorability is good, I think. I didn’t think of averages as areas before, but now this video will come to mind when I work with areas. The motivation is the weakest point, I think. It’s not clear why we need all those averages. There is some reasoning in the beginning, but it doesn’t explain why the arithmetic mean, for example, couldn’t be used for all those examples.

Awesome choice of topic! Great animations! I see on youtube that I’ll not be the first to point out that your sound design has issues, so I won’t harp on that, but 5:41 is notable. The formulas and the shapes morphing into each other is not great: seeing them at the same time could have been far more useful in helping to understand and remember the patterns. All that wasted empty space at 11:11 where you could have shown the shapes. The notation Area_i could have been avoided, we didn’t have time to remember which is which.

This video provides a solid visual intuition for why a set of mean inequalities exist which is exactly what a video is supposed to do. Though the ideas provided in the video were great, the execution of the video could use some work. The sound effects were sometimes louder than the speaker, and the high pitched sound effects were grating on the ears. Nice method, and I think the video-making process will improve over time.

This was a fun video to watch, and I think it would be a cool task for a middle/high schooler to try to explain the inequality geometrically to get practice with that sort of thing. However, it wasn’t clear why the geometric proof provides additional insight; what do I miss if I stick to an algebraic proof? And though you explain where each type of mean is used, it wasn’t clear why you would care about which mean is bigger or smaller. And though you explained where each mean was used, I was left wondering why exactly certain means are preferred in certain fields. Maybe if you phrased it as a fun problem to solve, and paused to let the viewer try to figure things out themselves every once in a while, it would become more like an engaging try-solving-this-problem video. I really enjoyed the idea!

Some audio issues but the visuals were clear enough to understand despite the echo in the audio.

This video was very interesting and clear, but I think there are definitely places to improve. I can see everyone talking about it in the comments which I presume you’re probably sick of by now, but the sound effects were definitely too loud. Personally, I wouldn’t include them in a video, but I can see them adding a bit of pizzazz, but yeah definitely turn them down. I really liked the quality of the manim issues. There were a few technical errors there, but nothing major. I’ll list the timestamps at the bottom where there’s issues with choreography in terms of mic quality changes, manim, or whatever (not to have a go at you, but just so you know what a viewer sees and doesn’t see. Do bear in mind I’m looking out for this kind of stuff). Really, these were just minor errors, and I think you are very close to making some very high quality videos. It’s more the presentation than the communication or content that’s holding you back, and by adding some background music and fixing up some technical errors, I would have no reason not to give this video at least a 7.

#Errors: 1:51 - The AM GM … all overlap when transforming 1:57, 2:17, 5:58 - Arguable whether these matters but the inequalities don’t fit after transforming, so they transform then move, but I feel like if you could somehow make the inequality signs move whilst the transform is happening? Maybe it could be done with an animation group and lag ratio, but there may be a good reason for why it’s like that. (Coming back to this point after adding a couple more timestamps, I can see this happening multiple times, so I assume it’s merely a preference for you) 3:55 - God knows how I managed to see this (only on the second time round), but the line y = x clips over the other for some reason, but I really don’t care about this since there is no way anyone is going to see that (even though I did, maybe I just had spidey senses or something) 4:37 - Area_1 appears on the far left for some reason 4:52 - I’d get rid of the previous a and b labels on the x and y axis because obviously that overlap doesn’t look too good 5:41 - Mic quality change 6:52 - The 3 in Area_3 is not a subscript, and is just a normal 3 7:29 - There’s a whole sequence of animations where the x and y start overlapping the c’s, and then overlap everything else. I can’t really say much more about this though because I don’t know of a workaround. 7:41 - the a/2 and b/2 snap to a different position 7:56 - the two arrows are different sizes (again I don’t know how to fix this one) 8:12 - the arrow teleports up after moving down, and the same for the other arrow 9:02 - the two shapes’ labels overlap each other

I wouldn’t get too worried over these mistakes as I’m sure most can be easily fixed and I can’t ask for perfection, but this is a very good video. Well done!