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:    • Euler's Formula Beyond Complex Numbers  
Patreon:   / 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


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This video was generously supported in part by these patrons on Patreon:
Marshall Harrison, Michael OConnor, Mfriend.


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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


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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/mor...