Introduction to Projective Geometry

Juan Carlos Álvarez Paiva


Here ends our rapid survey of some of the classical results of projective geometry. We will elaborate further on these results throughout the course, but more importantly we shall see how they relate to other domains of mathematics such as linear algebra, group theory, the study of quadratic forms, complex analysis, hyperbolic geometry, and topology. Many of these interactions will be found in the appendices of the notes de cours. I will be adding them as time and energy permits.


In preparing this interactive course on projective geometry, I have made extensive use of a great quantity of software that is, for the most part, freely available through internet. Indeed, it was the disponibility of this software that prompted me to undertake this experiment. I warmly thank the developers of Emacs, Linux, TeX, LaTeX, LateX2HTML, GIMP, Perl, HTML, XFig, and Cinderella (the only package that is not free) for the wonderful tools they have created. I hope that other geometers will also be tempted to experiment with them and will make their work freely accessible through the internet.


In preparing this lecture, I found the following texts very helpful:

  1. M. Chasles, "Traité des Sections Coniques", Gauthier-Villars, Paris, 1865.
  2. F. Klein, "Vorlesungen über Höhere Geometrie", 3rd. Edition, Chelsea Publishing Company, New York, 1957.
  3. Kline, M. "Mathematical Thought from Ancient to Modern Times", Oxford University Press, New York, 1972.
  4. M. Kline, Projective Geometry, in "Mathematics: An Introduction to its Spirit and Use", Morris Kline (Ed.), Scientific American, 1979.
  5. J.-V. Poncelet, "Traité des Propriétés Projectives des Figures", Gauthier-Villars, Paris, 1866.

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