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The famous Euler’s Formula for complex numbers provides an elegant way to describe 2D rotation, but is there a way to make it work for 3D or higher dimensions?
Previous video about complex numbers: https://youtu.be/4KlvI_uK9zs
3Blue1Brown’s video on the matrix exponential: https://youtu.be/O85OWBJ2ayo
=Chapters=
0:00 – Intro
3:03 – 3D vs 2D
5:07 – A Brief Overview of Matrices
8:47 – How To Exponentiate a Matrix
12:06 – 3D Rotations via Matrix Exponentials
17:54 – How to Build Rotation Generators
24:54 – 3D Euler
27:10 – A Look Ahead
28:25 – Brilliant ad
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CREDITS
The music tracks used in this video are (in order of first appearance): “Checkmate”, “Dream Escape”, “Ascending”, “Rubix Cube”, “Orient”, “Falling Snow”
The track “Rubix Cube” comes courtesy of Audionautix.com
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This video was supported in part by these patrons on Patreon:
Marshall Harrison, Michael OConnor.
To support future videos, become a patron at https://www.patreon.com/morphocular
Thank you for your support!
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The animations in this video were mostly made with a homemade Python library called “Morpho”. If you want to play with it, you can find it here:
https://github.com/morpho-matters/morpholib
