I recently came across Ancient Greek Geometry, a web toy by Nico Disseldorp, and it got me wondering: is there a way to exactly model the points generated by geometric constructions, starting from two distinct points, in a way that allows performing computations on them?
I would need finite representations of:
- lines specified by two points, and
- circles specified by the center and a point on the circumference
such that the intersection points of any two constructible objects can be computed. Though objects do not need unique representations, it must be possible to compute whether two representations refer to the same object.
Is there a way to represent constructible points, lines, and circles in this way?