> I have never seen someone try to use Pauli matrices to solve a trigonometry problem, but it can certainly be done.<p>The Pauli matrices in this context are isomorphic to quaternions, which certainly have been used to solve geometric problems in 3 dimensions (although not necessarily by physicists), as has been discussed many many times here on HN. The property of describing spin-1/2 particles (i.e. generating SU(2)) is precisely the same property that makes the quaternions amenable for use in reasoning about 3D rotations!
Somewhat related: How many of you have ever seen the green flash [0] ? I never have unfortunately even though I've looked for it many times.<p>[0] <a href="https://en.wikipedia.org/wiki/Green_flash" rel="nofollow">https://en.wikipedia.org/wiki/Green_flash</a>
> If the earth was flat, photographs of the sun setting over water would look like this:<p>I am curious: has this argument, historally, ever been used against the idea that the world is flat?
Sebastian Lague made a fantastic video about approximating/simulating Rayleigh scattering in real-time (using Unity) to simulate sky color and sun sets. Really interesting stuff<p><a href="https://www.youtube.com/watch?v=DxfEbulyFcY" rel="nofollow">https://www.youtube.com/watch?v=DxfEbulyFcY</a>
Does geometric algebra provide an alternative to pseudovectors for representing things like angular velocity?<p>The fact that you have to flip the sign of pseudovectors sometimes feels like a hint that they aren't the right representation, somehow.