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 to me and mentioned " I came across it in a book I found online titled 'Mathematical Puzzles' by Peter Winkler. There, it is attributed to Nathan Bowler"
Corrections:
Near the end, 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 different internal angles.
Also, when the formula for the 3x3 determinant is shown, it seems the "c" got swapped out for a second "d".
I referenced quaternions at the end, and if you're curious to learn more, here are a few options.
This video walks through concretely what the computation is for using quaternions to compute 3d rotations:
https://youtu.be/-zsnHbQyRnc
This is a nice talk targetted at game developers:
https://www.youtu.be/en2QcehKJd8
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:
https://youtu.be/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
SEV#3: https://youtu.be/vXBtyYvMx24
------------------
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
------------------
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.
Mailing list: https://3blue1brown.substack.com
Twitter: https://twitter.com/3blue1brown
Instagram: https://www.instagram.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Website: https://www.3blue1brown.com