This article by Simon Altman on #quaternions and rotations may be the most lucid i've seen on the topic: https://worrydream.com/refs/Altmann_1989_-_Hamilton,_Rodrigues,_and_the_Quaternion_Scandal.pdf
My beloved #spinors are also mentioned. It is rarely explicitly stressed that the quaternionic imaginaries are 180° rotations, not 90° rotations. The same *can* be said of the complex numbers too of course, but commutativity makes things special there.
)
P.S.
I couldn't work out in my head what would be an appropriate order in which to enumerate the vertices of a four-dimensional hypercube given e.g. by
α+βi+γj+δk
where each of the Greek letters is 0 or 1.
And he sketched a crooked tesseract.
Project complete!
https://quaternion.cafe/ is a "vim-style" interactive tutorial that teaches sensor fusion with quaternions. It's mostly an aggregation of stuff I learned over the past few years while messing with inertial sensors.
How sad. Freya Holmer @acegikmo used to post on masto, but I missed this:
https://www.youtube.com/watch?v=PMvIWws8WEo
And her page now points to a bluesky account 😕
Another Thursday project idea for formalizing stuff in Mizar: The Icosians!
The Icosian group is isomorphic to the binary icosahedral group, but built out of quaternions.
We can use them to form a ring, also (confusingly) called the Icosians.
You can then form a lattice out of them, and it's isomorphic to the root lattice for the E8. It's really quite amazingly beautiful!
#Mizar #Quaternions #Icosians #ProofAssistant #E8 #Lattice
https://thmprover.wordpress.com/2025/01/02/icosians-in-mizar/
The brilliant story behind quaternions:
#mathematics #vector #analysis #quaternions #science
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