Can you guess a shape from its shadows?

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 #SoME3