Our journey is coming to a close. What have we learned, and where do we go next?
## Bibliography
1) ***Projective Geometry*** -- Harold Scott MacDonald Coxeter -- 1974
2) ***Perspective and Projective Geometry*** -- Annalisa Crannell & Marc Frantz & Fumiko Futamura -- 2019
3) ***Foundations of Projective Geometry*** -- Robin Hartshorne -- 1967
4) ***Perspectives on Projective Geometry*** -- Jürgen Richter-Gebert -- 2011
5) ***The Four Pillars of Geometry*** -- John Stillwell -- 2005
## Further directions
If you’d like to explore projective geometry further, here are some topics that we didn't get to in this course.
1) *More drawing challenges*: In addition to the ones we used in this course, Crannell, Frantz, and Futamura have many more in their book Perspective and Projective Geometry.
2) *The Synthetic Analytic Equivalence Theorem*: Hartshorne's book develops and proves this, and is quite accessible.
3) *Projective geometry over an arbitrary field*: the axiomatic approch of Coxeter provides a wonderful introduction.
4) *Conic sections*: You might not expect curvy conic sections, like ellipses and hyperbolas, to come up in projective geometry, and yet they do! For example, five points determine a conic, and given five points in the plane, we can generate arbitrarily many more points with just a compass and straightedge! Richter-Gebert's book explores this side of projective geometry.
5) *Projective duality and polarities*: There's much more to say about duality, and we can construct dualizing maps between points and lines, known as polarities. These are explored in detail in both Coxeter's book and Richter-Gerbert's.
