Summer of Math Exposition

This video is an enjoyable watch, and I left the video thinking about how cool the Lemniscate constant is. The dialogue between the main narrator and a second, more naive character I think is a good addition, and almost takes the role of a mouthpiece for the viewer expressing their questions.

As an overview of the constant I think it does a very good job and highlights the similarities between the Lemniscate constant and pi, however each time I’m always left with the question of why. Why is the continued fraction this? Why is the infinite product this? Why are the polar coordinates that? While I did leave the video with the impression that they are more deeply connected and that it’s not a coincidence, I feel like this would be stronger if we at least got some sense as to how these are obtained, even if a brief overview.

Music was great, but there are sections it could have been silenced

Not a fan of the unnecesary 2nd speakers commentary Benefit of 2nd speaker - gives pause to see whats on screen Downside - unnecesary, annoying, slows progress, disrupts flow of 1st speaker.
alternative option - circle sections and make minor commentary as 1st speaker. (I don’t have a problem with the 2nd speaker’s voice, just with their short and often useless commentary, which keeps interupting the presentation)

5:09 - I think this part could have used a statement that the visuals were “simplifying the algorithm”

6:30 - squircle COOL

7:40 - Gauss’s constant 👍 (defined as the reciprocal of the arithmetic–geometric mean of 1 and the square root of 2) another visual diagram for this -> https://www.instagram.com/reels/DM81_5UoEMX/

every time you say now I kept hearing “NO”

3:28 “they are nearly identical” - was great opportunity to elaborate the differences

10:30 - length of a sine curve COOL

1-9 Motivation: 2 (could have used a summary of the article in the begining, “all the topics that you’ll learn about in this presentation”) Clarity: 8 Novelty: 1 Memorability: 3 14/4 = 3.5

That was fun! Would have wished for a bit on why I should care about lemniscates in the first place, though.

Absolutely incredible video!

Nails everything. Love the story direction. Reminds me of the old Outside In video.

One thing I would say holding the video back is the “memorability”of the video. But this probably stems from lemiscate constant not having any practial applications shown in the video.

Pretty great video. We learned a lot of new stuff.

This is a well done and interesting video… Sound and brief explanations are good, but they can be improved. I mean there are many formulas that are a bit intimidating and deserve more explanations … In general, technically it is a remarkable work and the subject is interesting.

Novelty: I haven’t heard of lemniscate constant before, so I think this is novel. It’ neat. Clarity: quite a few complicated formulae are rattled off… but it might not matter, part of the goal is to show how many similarities it has with pi, not understanding and deriving these. Memorability: I’ll probably remember that this leminscate constant… exists. But that was the point so I think the video is successful.

The dialog with 2 people… maybe you could practice a little more, somehow this format didn’t quite sit right with me.

The opening reminded me of this: https://www.youtube.com/watch?v=Zv-XNlE1s8E Thankfully doesn’t go in the same direction.

I had never heard of the lemniscate/lemniscate constant before. I don’t particularly understand it yet, but the video did a nice job of giving several aspects to approach learning about it further which is nice.

Pretty interesting. Once you start to look you watch it until end.

Great animations and great pace.

Suggestions for improvements

The dialogue felt constructed rather than natural. Either skip the dialog and have a single narrator, or make the dialogue natural.

Keep on doing what you do. I wish you the best.

Well motivated, and interesting.

I think this is a good introduction to the constant. I think for the audience of this video, who would be more familiar with inifite sums/products/continued expansions, it could be better to instead focus on one idea, rather than listing all the general connections here.

I think it’d be cool to see a detailed connection besides the lemniscate vs pi that delved into a parameter of other constants deriving from the same connections here, to understand more about the behaviour of things.

really like the story telling approach,but the transitions can be improved.

Feels like the deranged ramblings of a mathematician. I love it.

Nice job on this submission. This video reminded me of what it felt like when I first learned about this constant that I stumbled upon from specific definite integrals. The narrative structure as a dialogue between two characters is nice in making the mathematical concepts more approachable and coversational, and you systematically revealed the mirrors between the lemniscate constant and pi in a clear and interesting way, highlighting some important and deep connections. The only things I think could be improved is levelling out some of the audio to make it sound more seamless between the both of you, and the final third felt like a rush of identities without fully digesting the geometric mechanics or reason why they arise.

Beautiful video. Nice topic, amazing examples and visualizations. Keep up the good work

Indeed I did not know about this constant before! The visuals, language and pace are typical and appreciated. The content too was interesting, but in the sense that each bit/part was. I feel rather left out because the whole thing is lacking structure, lacking overall progression and buildup. The music was ok after all. The dialog made the mark rise by some amount ;)

This was just overall a really great video. The concept is certainly well motivated and novel, and did a really good job at explaining the concepts.

Very cool, I hadn’t come across this number before. Well paced video, and not too long. It held my interest the entire time. I liked the back and forth conversation style, that helped it to maintain flow and avoid feeling like a lecture. Be careful with some of the English pronunciations - when used as an adjective, it’s AIR-ith-MET-ic. And geometric is always JEE-uh-MET-ric. Btw I LOVE ‘Pomega’.

As the narrator in the video says this feels like a long list of equations and properties without much context or insight. From the video I do get the sense that the lemniscate constant may be interesting and/or useful but I don’t have much new insight. I don’t think that the back and forth podcast like narrative structure helped the exposition.

Hey I think the video is about an interesting topic and the animations were well presented.

I think the main issue I had was with the purpose and the narrative. I was never sure why I was being told things it seemed very confused and sprawling you jumped quickly around between topics often only flashing up equations and then flashing away.

Too many times I was told how to feel “Isn’t that amazing?” “that is beautiful” without actually telling me how or why. Why should I be surprised or amazed. It seemed too much like a tour of coincidences and not relaly and exposition of anything fundamental or meaningful.

Gamma function was possibly the only part I really thought was interesting and even that you assumed so much knowledge and insight.

At the end you even point out the issue with the video as a rattling off of equations. I enjoyed the information but I don’t think this way of narrating it was the best.

Great animations and voice recording. I wish the script had been more mathematical, and less “about math”. I don’t connect with these “sense of wonder”-type morals. Why not sketch a small proof, like an efficient way to compute elliptic integrals using AGMs ?

Hello! Welcome and congratulations on your first video. It’s a very nice deep dive about the pi brothers, I came out having learned more than I bargained for, it ended with a great message, spot on!

I like the conversation format, it definitely works to engage the viewer and makes the video approachable and relatable. I do think you could make it feel more natural in the future to create really nice videos. When you want to lead the topic somewhere different and force the format to keep going as it is, it does feel a bit unnatural. My personal opinion is, you don’t have to force it to be like that, and can diverge from the student/teacher conversation where it doesn’t fit right. It shouldn’t distract from the topic at hand.

The animations are nice, but I do think you can have more things going on on screen to sync better with your voiceovers, this will make it work better on YouTube, as people like things more flashy :)

This was cool! I’ve heard of the lemniscate constant, but I never knew what it actually was, and I had no idea it showed up in so many different places, or that it had so many similarities to pi.

interesting collection of facts

Really enjoyed this. Might have benefitted by omitting some concepts near the end - I felt like the discussion on the gamma function connection wasn’t clear to me. Loved the demonstration of the AGM. At 6:33 the 2nd speaker audio level came in really loud and was a bit jarring.