The Insane World of Polygon Packings

Let me show you some surprising things about how squares and other polygons fit into different spaces!
0:00 - Homemade Demonstrations of the Square Packing Problem
7:06 - Digital Images of The Craziest Square Packings
14:24 - Packing Other Types of Polygons
Here are the websites that I used images from:
erich-friedman.github.io/pack...
kingbird.myphotos.cc/packing/...
kingbird.myphotos.cc/packing/...
In the images I included, there are some notes attached (from the original websites). To clarify some terms: they use "s" to describe how many times longer the big square's side-length is compared to the small squares (or equilateral triangles), and use "r" to describe the radius of the larger circle in terms of smaller shapes. Most of the images also clarify whether they have been proven, or if they've just been found (which means they are the current best-known configuration but another weird arrangement could possibly beat them later).
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In case anybody searches any of these terms to learn about them, this episode is about some crazy geometry that some may consider cursed (and/or beautiful), related to the most efficient ways to pack certain polygons into shapes, such as square packings, triangle packings, circle packings, cube packings, combinations of those, and more!
This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.
Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.