What I found most fascinating about the explanations (I was in pre-calc at school at the time) was the math involved. During my classes (or any math class I've ever been in) they gave us formulas and equations but no meaning or real world context. If they'd told us how we could use the distance and angles to figure out what they'd figured out so long ago I think the math would have been much more interesting and brought home the point of why it is relevant to anything.