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.
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