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Math EE: Measuring Angles through Different Systems

So my school hosted an EE workshop today and after slamming a bunch of information into our heads we have less than 24 hours to hand in our EE proposal. Naturally, I'm still a bit leery on what would be a good idea to do. I'm thinking about doing a Math EE, and this is what I've thought up so far:

Topic: The measurement of angles through different systems

Research Question: Are popular contemporary angle-measuring systems more useful as mathematical tools as compared with now-defunct or less popular systems?

Now I've looked through some Math EE Reports of previous years, and I've noted that my best bet for getting a good mark is probably:

a) practical application

b) actually doing math

I have some ideas about explaining the sources of some systems; degrees, radians, etc; through math, as well as less common ones such as "points" (which is used in navigation apparently- real life application).

However, this seems way too simple.

tl;dr: My question is this: Does anyone know of any more complex (but potentially understandable for an IB student, of course) mathematics involving angles? Preferably of an uncommon angle-measuring system, although radians and degrees is cool too.

Oh yes, also, I'm not sure if this topic is actually any good at all. Any commentary on it would be appreciated.

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Hey! I am by no means a maths expert - seriously, I can't imagine writing a maths EE - but I'll try and give some useful advice. I think that whilst it's good that you've narrowed down your area of interest to something about esoteric angle systems, I think that your RQ is still too broad. So, for example, how would you define "useful"? And how many "contemporary angle-measuring systems" are you planning to look at? And I think you could specify which particular uncommon angle-measuring systems you are looking at - I'm not sure on the details myself, really.

Also, I think that focussing more on the practical applications is on the right track, as you noted.%2