Five puzzles for thinking outside the box

Geometry puzzles that benefit from shifting the dimension.
Bonus video with extra puzzles:   / 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:
   • Math in Game Development Summit: A Vi...  

This video walks through concretely what the computation is for using quaternions to compute 3d rotations:
   • How quaternions (4d numbers) visualiz...  

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:
   • Visualizing quaternions (4d numbers) ...  

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:    • Secret Endscreen Vlog #3  

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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/a...
https://open.spotify.com/album/1dVyjw...

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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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