Rational Trigonometry in Finite fields

I suggest you take a look at developing a small program to work through finite fields(prime ones to start with) where one can explore the number theoretic facts of the blue, red and green geometries of chromogeometry.

If you want to read up on this Norman Wildberger has many papers that will help get you going on this topic.

https://www.researchgate.net/profile/Norman_Wildberger/contributions