Brendan, your paragraphs are getting smaller, good! However, they need to whenever appropriate have an associated image, and that image needs to be linked to the paragraph clearly. Help Keith and Maria develop the needed technology.
"a device to absorb the sun's energy" such as?
"the angle the light beam makes with the perpendicular when it hits the parabola is equal to the angle it makes with same perpendicular after being reflected." Please show.
Math Exp: requires elem calc and trig, right?
"The fact that a parabolic reflector can collect light in this way can be proven.", i.e. [mathematical statement of what you're going to prove] Then Step 1, etc.
This is a nice thing to have and your treatment is good, too. I hesitate to suggest this to you since it would be nice to give somebody else a chance with this important, fundamental stuff, but do you know the echo bench in the President's Garden? If two people sit in the right spots (with a fair degree of latitude) and whisper, they can hear each other pretty clearly--it's elliptical and sound bounces from one focus to the other.