Models of the Real Projective Plane

by Egbert Brieskorn If you feel attracted by the beautiful figure on the cover of this book, your feeling is something you share with all geometers. "It is the delight in figures in a higher sense which distinguishes the geometer." This is a well known statement of the algebraic geometer Alfred Clebsch. Throughout the history of our science, great men like Plato and Kepler and Poincare were inspired by the beauty and harmony of such figures. Whether we see them as elements or representations of some universal harmony or simply look at them as a structure accessible to our mind by its very harmony, there is no doubt that the contemplation and the creation of beautiful geometric figures has been and will be an integral part of creative mathematical thought. Perception of beauty is not the work of the intellect alone - it needs sensitivity. In fact, it does need sensual experience. To seperate the ideas from the appearances, the structure from the surface, analytical thinking from holistic perception and science from art does not correspond to the reality of our mind and is simply wrong if it is meant as an absolute distinction. It would deprive our creative thought of one of its deepest sources of inspi ration."