This video explores the question of whether you can determine the shape of a 3D object by observing a few of its shadows. The results are surprising and beautifully rich!
I created the slides in PowerPoint, and I wrote the music using a trial version of Ableton Live 11.
For more on this topic, here are some resources from Hideki Tsuiki (@hidekitsuiki1551) :
- Video showing the 3D prints and their various shadows (Watch This!): https://www.youtube.com/watch?v=VQvyxG4X4iA
- Imaginary cubes webpage: https://u.kyoto-u.jp/icube
- Imaginary cube sculptures and Latin squares: https://archive.bridgesmathart.org/2010/bridges2010-159.html#gsc.tab=0
- Imaginary cubes and fractals: https://archive.bridgesmathart.org/2007/bridges2007-277.html#gsc.tab=0
- Imaginary cubes and packing puzzles: https://www.mdpi.com/1999-4893/5/2/273
- Imaginary cubes and hypercubes: https://link.springer.com/chapter/10.1007/978-3-319-13287-7_15
Special thanks to @feynmanschicken for offering feedback during the creation process.
0:00 - Introduction
2:48 - Imaginary cube patterns
4:32 - Latin squares
5:43 - The replacement trick
6:22 - Fractals
7:44 - Further exploration
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