The Italian Renaissance painters began to incorporate perspective into their drawings in the 1400’s, but our eyes naturally understand depth from the 2-dimensional image on the back of our eyeball. It’s this projection on the retina that allows mathematicians to represent field of view with the projective plane, and in this talk we’ll investigate what makes it so difficult to translate between
projective and 3-dimensional space. We’ll start with a review of how to build real projective space and it’s homology. From this construction we’ll present a model that will allow us to draw lines,
conics, and cubics in a meaningful way on the projective plane. In particular, we’ll demonstrate how to add using elliptic curves. We’ll then take it a step further to discuss its use in some modern crypto-systems and computer vision.