Summer of Math Exposition

Good presentation and animations.

I do think the VO is a bit too fast. You could afford to slow down a bit and let your explanations sit with the viewer for a little bit before moving on.

I liked

• everything could be understood from first principles
• the somewhat fast pace
• including the proofs for the more advanced theorem, as an exercise of sorts for the more advanced viewers I disliked
• motivation was lacking
• very few new connections to other topics
• what now? where does this lead?

The explanations were clear,however the pace made it feel like i was listening to an audiobook of a math textbook and less like a video explaining a topic.They could also have included more intuitive or visual explanations,or gone into more detail about the consequences of the properties of the pythagorean ttriplets.

Nice piece letting audiences know the information in details.

It’s interesting. Pacing/presentation/storytelling could be a bit better but the explainer feels clear nonetheless.

A fresh look at some math I knew before and hadn’t thought about for a while: I don’t think I’d heard about the rules relating to divisibility by 3, 4, or 5 before, that was an interesting addition, and I don’t actually know if I’d seen a proof for that form of the solutions before. I appreciate that you included a proof of the theorem for people who hadn’t seen it. (I actually had a similar one in my video, just one that included algebraic FOIL rather than being strictly geometric - yours is a bit slicker, I like mine just because we do end up getting to talk about FOIL more explicitly and that ends up being slightly important to my video.)

Overall, just nice and clean, not much else I think I can say. Well done.

A complete introduction to Pythagorean triples, very convenient for capable and motivated students. However, due to the lack of applied and engaging elements, it may become difficult to follow for students who struggle more. Since this project aimed precisely at helping those students, I cannot rate it much higher than satisfactory.

Video was okay. Some crucial parts felt bit rushed. For eg, while explaining the proof of pythagoras theorem using the geometry of squares and triangles, the video skipped over the part how the pink areas came to be. Another one, while explaining case 2 of the proof for different parities in primitive pythagorean triplet, I didn’t follow why z^2 should always be a multiple of 4 (which seemed to be a crucial part of the proof).

Further, the explanations feel dry and the video could use more visuals, specially the middle part.

The results you present are interesting, and you do a good job proving everything. But you present it as a list of facts, with no intuition for where they came from. How would someone have come up with any of these results? Also, vary your tone and pause between thoughts to keep the narration from blending together.

Great video! Fast and straight to the point, but also very clear.

Sorry, I do not feel this video brings something special compared to a book

I think that you had a nice idea, but I believe that some tweaks should be performed to get the result that you intend.

First and foremost, I have the feeling that you chose the wrong medium for your topic. Videos shine when you have many visuals that you want to show the audience to support the intuition or the understanding. In this video, however, you rely solely on text and formulae. As such, an article might have been better suited. This would allow the audience to ponder more easily without having to pause whenever they want to think.

The second thing I noticed is on the introduction: Your video claims to be on the generation of Pythagorean triplets, but the introduction is about number theoretical properties of triplets. That is really confusing. This make it seem more a list of results than having a real thread which an audience could follow easily. This feeling is reinforced by the fact that the video is really fast-paced, so that people not super familiar with this sort of proofs.

If you reframe your idea slightly and switch to a different medium, I think that your explainer could work really well, so please do not take the above too negatively!

Side note: in the proof on the parities, in the second case, it should be $x_1,y_1\in\mathbb Z^+$.