One of the other examiners is the head of our Math Ed program, and has taught her teachers-to-be some of this material. She offered to bring in the tools she uses for that, including, among other things, glass spheres and rubber bands. (The teaching tools have to be inexpensive, given the parlous state of high school budgets.)

Yeah, vector math makes things much easier. Part of the challenge of this task was actually reading Regiomontanus (in English) and translating what he said into modern language.