Quaternions
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So, the quaternions. I remember doing very little with them in my undergrad abstract algebra and that they came up in complex analysis in discussion once; but what fields actually use them?
Hehe, fields; pun intended. It's been 10 years since formal education for me; so the memory's not great.
>>7944163
that picture made laugh
i know i'm a loser
>>7944163
Quaternions are used often to describe rotations.
I've read a couple robotics papers dedicated to solving the Wahba problem via quaternions
>>7944163
rotations in 3d space.
I know they are used in 3ds max and such programs
>>7944487
also, 4 axis means no gimbal lock, unlike Euler angles
>>7944163
They are the one nontrivial element in the Brauer group of R, so any field dealing with Br's deals with quaternions, so algebraic geometry.
In differential geometry they pop up in the description of hyperkähler manifolds, and of course in endowing S^2 with its standard complex structure.
A whole bunch of the real clifford algebras involve quaternions, so there's your application in physics, representation theory, and algebraic geometry (last one via Kuga-Satake construction).
![Complex-Numbers-15[1].jpg](https://i.imgur.com/mPhPMhp.jpg "Complex-Numbers-15[1]")
