Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

The Kakeya Conjecture: A topological Rhapsody of the Rotating Samurai Sword

Audience:

Tags: topologytopology-algebra-geometry-fractals

This video targets the audience who are highly interested in Geometry and Topology, and whose math level is around high school level. I've work 3 months for this video, completed it using manim coding and video editing, all of those done by myself (I'm a 16-year-old Chinese high school student). This video introduces the Kakeya Problem, Basic dimensional knowledge, and the Katz-Tao Program to solve the Kakeya Conjecture, and the basic approaches Wang Hong and Joshua Zahl published in their paper claiming that they proved the 3-dimensional Kakeya Conjecture. I want to start from a really fundamental and anti-intuitive problem to lead the audience learn deeper about geometry and algebra, and understand how mathematicians worked their way to the success of proving a math problem. I believe this kind of video is educational. Although I learned all the manim and python techniques on my own, I managed to finish this 23-minute-long video. This is my first video, and for the standards of this, I'm quite satisfied, and I sincerely hope that you can recognize my video. Thank you.

Analytics

5.3 Overall score*
101 Rank
14 Votes
6 Comments

Comments

5.2

THis was hard to follow at times. No wrtiten words, only audio when describing equations or referring to volume or area. You can also go much faster.

6.5

I liked the pace, animations, and the script is nice.

Maybe there is room for improvement in the narration, but well done !

7

Great work, I can’t believe you are 16. I encourage you to make other videos, I admire you. Here in Europe the average math student can understand this at age of 23-24. This is the reason I can’t use your contents for my students at high school, but I’m happy to know that somewhere in the world there are smart people :)

7

Pretty good. A bit niche, but could yield something really good in the future. And very well presented!

4

Good first video! Interesting topic, and very well made animations.

Here’s some feedback:

  • The music is a bit loud, and makes the voice hard to hear.
  • There were lots of animation glitches, headings popping in and out where they shouldn’t.
  • It would be good to emphasize the difference between convex and concave shapes, because that might confuse some viewers.
  • The translation theorem seemed a bit unintuitive for me, so it would be good to see some more animations of that. Like a line getting translated through increasingly small areas. Also, when the line translates across the Peron tree, doesn’t it need an infinitesimally small section to rotate through?
  • I think worth noting that the answer to the problem isn’t “0”, but actually “arbitrarily small”, right? So your shape can be as small as you want, but still must be non-zero.
  • The explanation lost me in the second half by talking about Kakeya sets as sets of vectors with some dimension - I didn’t see how it related to the initial formulation of the problem with a line sweeping area through space.
  • In general I think lots of things in the second half could use more explanations and animations to show what’s going on.
8.4

Really nicely done.