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Re:Exponentially Better Rotations by enkimute on Saturday April 23, 2022 @02:44AM (#31131990)
These are also called the planar quaternions and are the even subalgebra of 2D PGA. I use and explain these (and their nD generalisations) in my SIBGRAPI 2021 talk on kinematics and dynamics in PGA.

https://youtu.be/pq9YfdPHhIo

There is also a writeup called 'may the forque be with you' available on bivector.net

Re:Exponentially Better Rotations by ogogmad on Sunday April 24, 2022 @10:57AM (#31144615)
Looks like there's been some progress on this front since I last looked.

Maybe Wikipedia needs to be updated.