Projective geometry is the geometry where every two lines have a unique intersection point. This is also the underlying idea of perspective which one can often find in the works of Renaissance artists. As it is characterised by A. Cayley, "projective geometry is all geometry" - since one can understand all other types of geometries (affine, Euclidean, spherical, hyperbolic, etc) as special cases of projective geometry.

Some of the possible things to study in the project would be

• Classical theorems of projective geometry (such as Pascal's, Brianchon's, Pappus, Desargues's theorems);
• projective duality;
• projective geometry and perspective;
• conic sections;
• hyperbolic geometry via projective models;
• pentagram map.

Prerequisites: Algebra II.

Resources:

There are many nice books (or book chapters) on projective geometry. You may start with the following:

• Nigel Hitchin, Projective geometry.

You will find more references here.