Symmetry and Pattern in Projective Geometry


Projective geometry had its origins in a problem faced by the painters and architects of the Renaissance: how to represent, by ‘projection’, the three-dimensional world in a two-dimensional drawing or painting. The mathematical ideas that were developed from these beginnings led to a kind of geometry of great elegance, that has quite a different flavour from the more familiar ‘Euclidean’ geometry. Intricate and surprising structures unfold from a very few, very simple concepts. It has been among my favourite mathematical interests for a very long time. I wrote this book because I wanted to convey to others some of the fascination I feel for this subject. It’s not a ‘textbook’. It is a collection of ideas that have especially appealed to me, presented in a way that emphasises general principles and that, I hope, will make you want to explore further.