Presentation

[stoutfellow]

The second of my Senior Project students for this semester made her presentation yesterday, and did a fine job. The title was Regiomontanus and Spherical Trigonometry; the presentation consisted mostly of proofs of the spherical versions of the Law of Sines and the Law of Cosines. The mathematics wasn't particularly difficult, but it did require considerable powers of visualization - enough so that one of the examiners had some difficulty with it - and there was a fair amount of case analysis involved. I was especially pleased with how she handled that. Typically there were three cases, depending on whether the angles involved were acute or obtuse, and each required the construction of several auxiliary points and arcs. Each time, she laid out the constructions in all three cases first, and then carried out the rest of the proof, which was essentially the same in all cases. This was neat and economical, and thus aesthetically pleasing. The examiners asked for some minor typographical corrections, improved diagrams, and - in an appendix - some background material, but otherwise her written paper was excellently done. I'm proud of her.

Comments

[selenite.livejournal.com]

I've gotten some good use out of spherical trig but it's not easy. I wound up dealing with most such problems as vector math. There is a lovely tool for them I saw at MIT, never seen elsewhere: a chalkboard globe. Think a 2.5 ft diameter globe with a couple of pivoting circles holding it as a frame. Made it very easy to visualize orbit problems.

[stoutfellow.livejournal.com]

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.

[selenite.livejournal.com]

At TRW I wound up using magic marker on tennis balls a few times. The 3-D orbit analysis software was only useful when I'd already figured out what I was looking for.

[stoutfellow.livejournal.com]

The third examiner - the one who was having trouble visualizing - did bring along a tennis ball, and my student tried drawing on it with chalk. Didn't work very well...