Sunset Geometry (2016)

> I have never seen someone try to use Pauli matrices to solve a trigonometry problem, but it can certainly be done. 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…

Bravo. A very nice article comparing and contrasting standard trig methods and geometric algebra methods. And as a bonus, it compares both with Dr. Wildberger's Rational Trigonometry. (Side note: I've known a few Australian mathematicians who embrace some very non-standard methods in mathematics, and I think it's great. We need people to shake up our thinking bout Math every once in a while.) A very nice piece for some relaxing weekend recreational math.

I found this to be a very gentle introduction to GA, FWIW: "Geometric Algebra for Electrical and Electronic Engineers" > This tutorial paper provides a short introduction to geometric algebra, starting with its history and then presenting its benefits and exploring its applications. > Abstract: In this paper, we explicate the suggested benefits of Clifford's geometric algebra (GA) when applied to the field of electrical engineering. Engineers are always interested in keeping formulas as simple or compact as…