Summer of Math Exposition

It's great,infact very intuitive topic it has done all of the steps which many misses but at same time the landscape is not formed where the arguments become obvious and that's it all is...

I had difficulty following all of the facts you introduced in the first few minutes of the video. Once you proved the volume of a 4d sphere, I started to see how these ideas are connected. Things went smoothly from there.

I like that the video goes through the material slowly and deliberately. However, I may be missing something, but part of the argument seems to be wrong or incomplete. I'm not sure that the the statement at 6:50 is true. If X and Y are distributed uniformly in [0, 1] and x^2 + y^2 < 1 then X^2 + Y^2 is distributed uniformly in [0, 1]. If it is true, it's not obvious to why it would be. Adding two random variables results in us convolving the two probabilities distributions. Then we combine that with squaring the random variables and the requiring that the result is less than 1. It's unclear to me that this would result in a uniform distribution.

no opinion I am puzzled by if "x²+y² >1 or z²+w² > 1 then "x²+y² + z²+w² > 1" Perhaps I have difficulty to understand I quote "about the same" by default

Disclaimer: I rated your SoME entry as "notably worse" when compared to the typical math video. This is just my own opinion, please do not take it as an assessment of your work's value. Hi! I think you did a wonderful job in research, animation, and narration. However, I am afraid your lesson does not work very well in the video format. It presents way too much material with way too many omitted details. Something like that would suit a textbook or, perhaps, a blog post, assuming a reader has a notebook and a couple of hours to derive all intermediate results by themselves. I am sure making this video made you understand the topic very well (and that is very valuable by itself), but please be gentler with your audience the next time. A few technical details: - Apologies for being pedantic, but spheres do not have a (nonzero) volume, balls do. - The video claims to rediscover n-ball volume formulas (including for n=2) but then suddenly pulls elementary results out of its sleeve as if they were axioms, which *feels* as circular (no pun intended) reasoning.

Generally a good submission. I liked the problem. It would be better to explain why some stuff doesn't work. For example, why we cannot use the same argument we used for x^2+y^2 for x^4+y^4. Or why we can't break down x^2+y^2+z^2 to (x^2+y^2) + (z^2) I would remove the basic introductions from the video (Like the definition of cumulative probability) and add these things. The length of the video could be shorter as well. Like 15 minutes is enough.