Projective Plane vs. Reference Plane I was told that the Projective Plane was also known as the Reference Plane in Projective geometry, but when I told my professor this, he freaked and told me I was completely wrong.  He said that the Projective plane is the lines that go through the origin that intersect the Reference plane at a point.  He said "a 'point' in the Projective plane is a line", and  "even though they look like lines, they are called 'points'"... 
This is word for word what he said, and he is the one grading my presentation.  So I am going to believe what he says, but I still don't understand this idea and the fact the Projective plane is NOT the Reference plane in Projective geometry.
Thanks in advance! 
 A: I am not sure that this is what you are asking, but it seems that you are talking about two different models for the projective plane.
One can develop projective geometry from a completely synthetic viewpoint, which means that you prove theorems using basic axioms without ever referencing to what the points actually are.
Now, projective geometry can be seen in (at least) two ways. The first way is imagining the regular two dimensional euclidean plane, and adding a "point at infinity" for each set of parallel lines. This means that parallel lines will all meet at the same point at infinity (but a different point for each parallelism class). This seems to be what your teacher called the "Reference Plane" (although I have never heard that terminology, and google doesn't seem to give many results).
The second way is to call lines through the origin of $R^3$ points.
The link between the two models is easy to see, given the model of lines through the origin, you can map each line to the $R^2$ plane by taking its intersection with the plane $z=1$. The only lines that don't intersect the plane $z=1$ are those contained in the $xy-$plane, and they correspond to the points at infinity that we added in the previous model.
