Hanfried Lenz gave a classification scheme for projective planes in 1954,[6] which was refined by Adriano Barlotti in 1957.
One of the simplest is based on special types of planar ternary ring (PTR) that can be used to coordinatize the projective plane.
[8] In a Desarguesian projective plane a conic can be defined in several different ways that can be proved to be equivalent.
In non-Desarguesian planes these proofs are no longer valid and the different definitions can give rise to non-equivalent objects.
[9] Theodore G. Ostrom had suggested the name conicoid for these conic-like figures but did not provide a formal definition and the term does not seem to be widely used.