If you want to understand quaternions better, try this amazing guide: https://eater.net/quaternions
#math #maths #mathematics #quaternions #modernalgebra #algebra #abstractalgebra #computergraphics #beneater
Reworked the 24-cell sketch, much easier to understand now.
Every one of the 12 visible #spinors has a button that brings the yellow spinor (the 1 state) to the clicked one because in 3D spinors double as rotations. (both are #quaternions so there exists a quotient between spinors, which is a rotation).
I think what's clear is that thinking in terms of a spinorial/rotational lattice makes things much easier to grasp than in terms of a vectorial/translational lattice
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.
Petrichor ᚄᚔᚅᚐᚁᚆᚃᚒᚔᚂ
Greg Spradlin
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❀𝓪𝓵𝓬𝓮𝓪𖤐 
Vassil Nikolov | Васил Николов
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