2024-11-08

[public] 380K views, 20.3K likes, dislikes audio only

3Blue1Brown

A series of delightful geometry puzzlesBonus video with extra puzzles: https://www.patreon.com/posts/115570453

The artwork at the end is by Kurt Bruns

Thanks to Daniel Kim for sharing the first two puzzles with me. He mentioned the earliest reference he knows for the tile puzzles is David and Tomei's AMM article titled "The problem of Calissons."

The idea to include the tetrahedron volume example was based on a conversation with Po Shen Lo about these puzzles, during which he mentioned the case of one dimension lower.

I received the cone correction to the proof of Monge's theorem from Akos Zahorsky via email. Also, the Bulgarian team leader Velian Velikov brought up the same argument, and just shot me a message saying "I came across it in a book I found online titled 'Mathematical Puzzles' by Peter Winkler. There, it is attributed to Nathan Bowler"

I referenced quaternions at the end, and if you're curious to learn more, here are a few options.

This is a nice talk targetted at game developers:

https://youtu.be/en2QcehKJd8

This video walks through concretely what the computation is for using quaternions to compute 3d rotations:

https://youtu.be/-zsnHbQyRnc

My own video on the topic is mainly focused on understanding what they do up in four dimensions, which is not strictly necessary for using them, but for math nerds like me may be satisfying:

/youtube/video/d4EgbgTm0Bg

Also, one of the coolest projects I've ever done was a collaboration with Ben Eater to make interactive videos based on that topic:

https://eater.net/quaternions

Timestamps

- 0:00 - Intro

- 0:32 - Twirling tiles

- 6:45 - Tarski Plank Problem

- 10:24 - Monge’s Theorem

- 17:26 - 3D Volume, 4D answer

- 18:51 - The hypercube stack

- 25:52 - The sadness of higher dimensions

Corrections:

18:49 - The formula for the 3x3 shown is messed up. The "c" got swapped out for a second "d", and the signs are wrong. (There was a silly bug in the code generating it)

25:10 - I mention the "squished cube" shape involves 6 copies of the 60-degree, 120-degree rhombus from the beginning. This is not true, the rhombuses in that projection of the hypercube cell will have internal angles of ~109.5 and 70.5

SEV#3: https://youtu.be/vXBtyYvMx24

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:

https://3b1b.co/faq#manim

https://github.com/3b1b/manim

https://github.com/ManimCommunity/manim/

All code for specific videos is visible here:

https://github.com/3b1b/videos/

The music is by Vincent Rubinetti.

https://www.vincentrubinetti.com

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.

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