Those are pretty nice, and can be done at a fairly low level (say, from 12 years old onwards) :
- The proof of the formula "half base times height" for the area of a triangle, by first considering a right triangle and completing a rectangle, then considering an arbitrary triangle and breaking it in two along an height (two cases : inside(+) or outside(-)) : it is a nice example of how mathematicians treat the general case by reduction to particular cases ;
- Euclid's proof of the pythagorean theorem using the previous formula, as in this animation.
