Summer of Math Exposition

Great video, as usual. The artstyle is amazing, the topic is original and the execution is brilliant. The only thing I would suggest for the future is to use some background music. I think music can be useful for building a certain feeling about the thing you are presenting and without it it's a bit... stale? Nonetheless good job!

Really enjoyed the subject and presentation ! I feel like i would like to have more time maybe for eatch explaination to make sure i understand but anyways xD. As an exemple, i am unsure about the meaning of a valley or mountain pole. The only thing is for the little note you put on screen, maybe give us a little extra time to pause the video ^^'. But overall the subject was interesing, the way you presente it was pretty clear and cool, even if i am not sure that middle schoolers will understand everything. I like how you managed to explain basics of origami and that it is and gives the "rules of origami". It seems pretty natural and the visuals help a lot. Can't wait to have the answer to the final question :)

Your visual style and the way you walk through the 3 proofs in this video are excellent. They feel completely intuitive with the visuals you’ve provided, with some caveats. I think that more explanation upfront about how the visual with the person walking along the paper in 2d means would help with grasping some of the later proofs. I also think a little more time should have been given to establishing the baseline rules and explaining the different kinds of folds. The images in particular make things a little confusing, as the paper is identical, and just viewed in a different way. I understand that is by design, but acknowledging that and explaining it more with slightly more complex patterns would go a long way. Finally, I think that the video could use a little more motivation. Origami is almost an inherently fascinating thing, so any amount of connection between these rules and how patterns are designed would be interesting and help the video significantly.

Very interesting video with some great math about a concept I had never really thought of before. My one criticism is that the pixel art style, which I think could work well for other videos, kind of harms the visual clarity in this case. There are a lot of points where it's hard to tell exactly what's being shown because of the pixelization, especially when there are lots of detailed diagonal lines which don't translate very well.

love the rhythm heaven feel

Loved the art style! Application and motivation were clear. Proofs were explained clearly (though the last one wasn't as obvious to me) The proof of two-colorability was the perfect kind of math "aha moment" where after you explain it, the answer is obvious in hindsight.

Very nice, cool animation style, simply shown concepts. It's a topic in math I haven't seen before either, but I feel like it can be nicely translated to Euler's work on graphs. Some of the diagrams for the third theorem were a little hard to follow and therefore distracting, but I was still able to understand the reasoning.

the last argument was a bit difficult to get a grasp on. i had grown familiar with the notation for a whole piece of paper, and I feel a bridge maybe could've been added between that notation and the new pole notation, so the viewer could get a foothold. very very good still!!

The pixel art is great, though in some places the low resolution makes things a bit messier - especially in the crane pattern where there are a lot of creases. It's not a big downside though, I'd say. I like the commitment to proving things visually. The alternating angles proof especially is really cute! I wish there were more of an overarching story, I don't see where the video is heading. It's more of a collection of random math facts about origami. These are interesting, but it would be good to have something to tie them together. One thing that confused me a bit were the partial creases in the crane pattern. In the other examples you give, we always fold the entire paper and so there is never a crease line that ends in the middle of the paper. Then I thought about how origami works and it made sense, but it confused me when watching.

I like the visuals and the proofs of the theorems are clear. Thank you! I didn’t see as much of the “why this matters” - is this useful at all for actually designing origami? Or what do people use this for?

An artistic work!

The pixel animation was good, but the last proof was not intuitive as the other two, very interesting to explore the math behind the origami and I was wondering what benefits or results can be derived after using this laws. I could be a great idea to see the applications behind these ideas. At the end of the video you left some questions about another restriction, can you extend the explanation of the question, because it wasn't clear why the border is a real problem.