Projective Geometry 5 Axioms, Duality and Projections

We discuss how projective geometry can be formalized in different ways, and then focus upon the ideas of perspective and projection. The interesting duality/polarity between points and lines also becomes apparent. In particular, we approach the following issues: The projective plane as an extension of the euclidean plane. The projective plane, described by homogeneous coordinates. Axioms for projective geometry (here I refer to the document: Projective Geometry, Finite and Infinite Brendan Hassett http://www.math.rice.edu/~hassett/RUS... ) The definition of perspectives, with respect to points and lines. The definition of a projection. How to find a projection between any 3 co-linear points and any other 3 co-linear points. How to find a projection between any 3 concurrent lines and any other 3 concurrent lines. This gets us close to the point of being able to discuss the fundamental theorem of projective geometry.