MSGSS
On the uniqueness of high school angles
The only first quadrant rational multiples of π whose cosines are of the form √k/n for positive integers are 0, π/6, π/2, π/3, and π/2. We will give two proofs of this fact: an ugly proof via Galois Theory, and the proof from the Book which exploits that 2\cos(aπ/b) is an algebraic integer. This is joint work with ChatGPT, and I will comment on that experience.