Summer of Math Exposition

Great layout of introduction -> examples -> exploration -> pattern-spotting -> proof. The animations are very good, and it is very digestible and motivated. However, this is a very well-covered area already (so much so that I think the “reflect trick” has become well-known).

Small nitpick - at 4:05, when you begin the animation of placing individual results into the grid, I would have liked this to continue at 4:12 (in a timelapse) to fill in the whole grid, instead of introducing the whole grid via patterns. That way the audience can first look at the whole grid and get a big picture, then you can adopt a “notice patterns with me” style.

The motivation was very clear and I like the animations showing the movements of the ball. I feel like this is not a video that a teacher would share with their students but a video that gives ideas to a teacher how to connect concepts like greatest common divisor and least common multiple to an interesting thought experiment.

However, I felt like some results were not really well explained and in the middle of the video one does only look at the grid with the solutions, which lost the visual appeal of the billiard table. The explanation and use of the prime factorization not well motivated in my opinion.