By orientation I mean roughly speaking whether we rotate clockwise or anti-clockwise. Formally I want to define relation $\sim$ between triangles (contained in the same plane) such that $\triangle abc\sim\triangle pqr$ iff enumerations of these triangles are both clockwise or both anticlockwise. Then I want to prove this relation is an equivalence relation and has exactly two equivalence classes.

I suppose all this can be done within Hilbert's axioms of incidence and order (no congruence, continuity or parallel axioms).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.