Summer of Math Exposition

Presented by 3Blue1Brown 3blue1brown

How to subdivide lengths (Build with prime numbers)

Audience:

Tags: number-theory

A couple of years ago I tried to light up a hallway I built in Minecraft, but I couldn't space the lanterns equally. This led to a problem in number theory that deals with all possible positive integer solutions to the equation L = an + bn + a, and a neat visualization to view all possible solutions.


Analytics

5 Overall score*
120 Rank
9 Votes
5 Comments

Comments

6.5

The video was very nice. I think that the cool motivation and clear result make this video memorable. The math also turn out to be very beautiful especially with the visualizations! The transformation between the motivation part and the more formal part was bit confusing to my taste. It was not that clear to me at the start what you consider “equal spacing” and that you want also equal spacing from the wall.

6

Cool! Something I’ve run into while playing minecraft as well. It is satisfying to see it solved out in terms of a simple but beautiful bit of mathematics.

I want to learn more about that fractal structure. What is it saying about divisors that it has that self-similar structure?

6.2

This was a very interesting problem found from a simple question that anyone could understand.

The outcome was very interesting and the diagram of how the pattern expands was great.

The narration was a little flat and the equations were on screen for too long. It would be better to try to animate the equations alongside the squares to hold the viewers attention and make it clear where the solution comes from.

It seems that more shapes or patterns could have been included for visual flair.

Overall this was an interesting choice of topic for a short video, but the execution felt a little bland.

5

I thought this had a surprising result from a fairly simple problem and pulled together some disparate topics. I’m not sure the motivation was very strong, and I think a high schooler would not be familiar with modular arithmetic. Presentation was good and the fractal-like image was very memorable.

3.1

The introduction confused me, as I couldn’t understand what the “right” form of lighting we were aiming for was. Also, you mentioned how the posts and edges were the same length, but the diagram showed that they were different lengths? You also didn’t very clearly define what posts and edges actually are. It got better the further into the video you got, but I was confused initially. I don’t want to hammer you for theirs entire review, because I did enjoy the section on modular arithmetic and the fractal-like pattern you came up with were very interesting and looked cool. I think this is certainly an interesting topic to explore, but there’s definitely some work to be done. Nonetheless, any video is better than no video, and I applaud your efforts. Well Done! I hope you continue to make videos.