This is a question on teaching.
I am teaching at this moment a course in algebraic geometry for master students on a very basic level. Today (this was the fourth lecture) I discovered that only four out of 20 students have ever seen the definition of projective space.
I would like to ask you if you know some nice, short notes that explain what the projective spaces are and that give some simple but still not tautological statements about them. A nice example that comes to my mind is Desargue's theorem, but I would like to have more of such statements. Maybe there are some theorems from classical plane geometry that can be proven using projective geometry? Even though I know what is projective space for almost 20 years I find a bit hard to find a good way to introduce and motivate it...