Interactive Course on Projective Geometry

Recommended Reading

Chapter one

1. Berger, Marcel, "Géométrie", Editions Nathan, 1990.

This is great book written by a great geometer. The quantity of illustrations and interesting remarks more than makes up for the references à la Bourbaki (see For chapter one, we will be following chapter one of Berger's book. Unfortunately, I'll skip the most interesting stuff there: tilings and platonic solids. But you don't have to skip it yourself.

2. Kline, Morris, Projective Geometry, in "Mathematics: An Introduction to its Spirit and Use", Morris Kline (Ed.), Scientific American, 1979.

This is a delightful little article explaining how projective geometry arose from the artists' need to represent 3-dimensional objects in a 2-dimensional canvas. It is very useful for finding out what projective geometry is about.

3. Weyl, Hermann, "Symmetry", Princeton University Press, Princeton, NJ, 1989 (original printing 1952).

The concept of symmetry finds its mathematical formulation in the concept of group and group action, but quite possible transcends this formalization. This beautiful book, written by one of the greatest mathematicians of all times, explores the application of symmetry in art, biology, physics, and mathematics.

4. Hoffman, K. and Kunze, R., "Linear Algebra", Prentice Hall, NJ, 1971.

A good book on linear algebra. You'll need one in this course.

Chapter three

1. Schwerdtfeger, H., "Geometry of Complex Numbers", Dover Publications, NY, 1979.

This is a delightful, and very complete, treatment of the geometry of the complex projective line and its ties to the geometry of circles and hyperbolic geometry.

2. Caratheodory, C., "Conformal Representation", Dover Publications, NY, 1998.

This beautiful little book is dedicated to interplay between complex analysis and hyperbolic geometry.

3. R. Penrose and W. Rindler, "Spinors and Space-Time", Cambridge Monographs on Mathematical Physics, Vol. I, Cambridge, 1984.

It's hard to decide whether Roger Penrose is a mathematician, a physicist, or an artist. Of course, these are not mutually exclusive occupations. In any case, the first chapter of this book is a beautiful exposition on the interactions of complex projective geometry and special relativity.