Summer of Math Exposition

Good animations, good brisk pace, and a fun open problem posed.

Really fun, dragged at time when you were just listing facts. The most interesting stuff was your own novel explorations of the longest pathing. Lean more into that kind of stuff, your interest is clear and it comes through way more than just saying facts about tiling/embedded triminoes in this video.

This video is well put together, and is engaging, with a well-written script. The humour is good, not excessive; that makes for a pleasant watching experience. Moreover the topic is easily understandable by a general non-technical audience. The music seems a bit too loud at some points, possibly more as the video progresses; it should be turned down, as it conflicts too much with the narrating voice. The pace is at times a bit too fast to be able to grasp the meaning of a sentence before the next one. Though this seems to have been done on purpose for the style of video that the author wanted to achieve. And in any case the topics are not complicated and are quick to understand. At times the video can be a bit boring or tedious to watch: when enumerating the ways tetrominos fit in pentominos and grouping pentominos depending on the results; and when classifying cells in pentominos by the number of neighbours. In addition, in this two cases it is very interesting to see how the pentominos are grouped together in the same way based on how many tetrominos, triominos they contain, and based on the number of cells that have a certain amount of neighbours. It feels like there should be a deeper reason for the groupings to remain together in such a way, and feels like an explanation (if known) or comment is missing. Maybe there is a geometric reason, maybe a combinatorial reason, or maybe it is consequence of the pigeonhole principle (subdividing a set of 12 elements in 4 subsets, in four different ways may have a reasonably high probability of resulting in sets all made from relatively few smaller subsets, especially since the constraints make this situation closer to subdividing the set in 3 subsets, in three ways). Further comments: I especially liked the proofs of the existence of infinitely many different tilings of the plane for the various pentominos: I liked the way it starts from the rectangle, then mentions that the argument works for any rectangle [small comment: in the case of a square the argument fails; for squares the answer depends on whether or not the cells are forced to be aligned to the grid or can be shifted by any amount (not multiple of the side length)]. Then shows that some pentominos can create rectangles, thus reducing the problem to the simpler case. Then shows that for other pentominos one can proceed by reasoning about lines, then generalises to diagonal lines. I really liked the flow from simpler to more complicated, and I really liked how the various proofs were grouped together depending on which of the arguments was used, thus giving the viewer multiple examples to understand a certain line of reasoning. In part 3 (drawing lines across all cells) I think the distinction between "having wiggle room" and being constrained to certain vertices should have been given a little more explanation to make sure the viewer understands the point that the author is making. And when saying that the T cannot have a line passing through each cell I think the author could have given an explanation for why (event just a quick and informal explanation, not necessarily mathematically precise). Final note: Despite the author not having a mathematical background, the video really seems to suggest otherwise. I do recommend that the author follow up on their passion for Mathematics either by taking a degree or by studying the discipline in their free time. Also, the author seems to have a clear talent for making engaging and understandable videos, and I believe they should consider to keep making videos.

This is a really fascinating video, your enthusiasm for investigating pentominoes really shines through in a way I find very charming. In many ways, your video reminds me of the work of someone like Fermat, where you have found this interesting area to explore and you've done as much as you can to navigate it through your own ingenuity. And, as a result, you leave a lot of enticing questions unanswered. I don't think that's necessarily a bad thing, I would love to see the follow-up videos by you or by others hopefully answering some of the questions you raise. I think one of your video's greatest strengths as a math video is the breadth of material you explore, you end up touching on topics like the lines touching every square that I definitely wouldn't have thought of on my own. I think this video is delivering a kind of experience that isn't what I would personally seek out on youtube, and that's making it a little difficult for me to come up with criticisms that I think are relevant to what this video is trying to do. I think one thing that I can say is I come away from this video feeling like I don't have much good reason to care about pentominoes in particular. It's clear that you do, and your enthusiasm carries me through the video, but after the video ends I feel like I don't have much else to latch on to. I think something that could help this is if you made connections between pentominoes and something else, perhaps other math videos that discuss similar topics, perhaps to some other common kind of puzzle or piece of media, just something that helps me to mentally place your pentomino facts into a bigger picture.

This is a nice exploration and presentation. The main thing that would make it stronger would be to provide mathematical reasoning why some of these facts are true, rather than simply observing them.

Very steady work, could be more interesting if one could extend tiling with more generalized shapes and higher dimension. Best part was the cat meowing in the end of the video.

Really creative. Explanations were easy to follow. Graphics were simple but effective. I found my self drawing squares afor a while afterwards. My old thanks you.

Wonderful!

I watched the video in full, despite at some point losing interest. I am nonetheless happy that I watched it in its entirety. It is better made than expected from your disclaimer and I know I could easily watch a video like this if the topic was more interesting to me. I lament the lack of maths in this videobecause and would've liked to see ways/ideas/algorithms on how to tackle and optimise the problems in chapter 8. I really admire your willingness to make the video out of the love for these shapes, I fully understand that and can relate to that, but as somebody with a mathematical background facts about the shapes just don't entice me as much without proofs or introducing new concepts. I am sorry, that I am rating your video so poorly, because it is a well-made video, it's just that it also has a very niche audience and that I don't really belong to it. I would encourage you to keep making videos, especially about things like Part 8 of the video, where you introduce your own 'game'. That was the most interesting chapter for me and I'll definitely have a go at it myself, although maybe from a more mathematical perspective on path maximisation and whatnot. Please don't be discouraged by my rating, there's a lot here to enjoy and while I may not be the audience for this video, I can definitely see myself being the audience for other videos like this that focus on different bits and go more into problem solving. Kudos for tackling this project, it is very well made for somebody's first mathematical yt video and I am very glad to see people without mathematical backgrounds enjoying shapes and games like this.

motivation 5/10 clarity 5/10 novelty 5/10 memorability 5/10 fantastic entry thank you

this could work nicely as a blog post, since the linking of ideas together isn't really here. all is useful info and would be lovely to reference in one place

As a math educational video, this was pretty average (not in a bad way). The topic was interesting. But it is the presentation that made this VERY interesting and catching. The humor was perfect, and the exposition both in animation and in delivery were just brilliant. Well done, I really want to see more of these videos from you! :)

Goal Orientation: 6/10 Novelty: 7/10 Thought-Provoking: 8/10 Comprehensibility: 9/10 Technological: 5/10 Overall Average: 7/10

Are there any real-world applications to this? If so that would be very interesting and it needs to be included in the Video. As it is, most people will probably get bored and stop watching pretty soon.

I don't know how much this fits the math theme, but this was fantastically enjoyable. I love how much passion you have about this niche topic!

What about a generalization of polyominos or some proofs? Nice animations.