# 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.

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 Dear Ellette, Could you give some information on the course you're taking? It might help people in formulating their answers. Regards, – Matt E Jun 1 '11 at 1:33

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.