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Curated by: Morphocular (20 videos)
Using a generalized version of Euler's Formula, exponential functions can be used to algebraically represent rotations in any dimension. But what is this generalized formula, and what can we use this representation for? Previous episode: https://youtu.be/Y1gOYtQYRXo Patreon: https://www.patreon.com/morphocular =Chapters= 0:00 - Intro 2:41 - Tilt Product Powers 5:13 - Generalized Euler's Formula Derived 6:57 - Classic From General 9:35 - Polar and Spherical Coordinates 13:20 - Trouble With the Matrix Exponential 15:56 - Computing Velocity of a Sphere Point 22:02 - Interpreting the Result 23:03 - Wrap Up and a Look Ahead =============================== This video was generously supported in part by these patrons on Patreon: Marshall Harrison, Michael OConnor, Mfriend. =============================== CREDITS The music tracks used in this video are (in order of first appearance): Rubix Cube, Checkmate, Ascending, Orient, Falling Snow. The track "Rubix Cube" comes courtesy of Audionautix.com =============================== The animations in this video were mostly made with a homemade Python library called "Morpho". It's mostly a personal project, but if you want to play with it, you can find it here: https://github.com/morpho-matters/morpholib