The following mathematical explorations serve as basic exploratory exercises in constructions and equation investigations. They are to be looked at with a very light heart,... less the scale of truth tip.
1 (sine)
2 (parabolas) / 3 (quadratic roots) / 4 (orthocenter's)
5 (a construction)
6 (rigid motions)
7 (ref & rot) / 8 (constructions) / 9 (rigid motions) / 10 (spreadsheet)