Abstract
Linear algebra provides an elegant way of introducing projective spaces over a field. Intuitively speaking, the projective spaces are the affine spaces to which a “point at infinity” has been added to each bunch of parallel lines. We study homogeneous coordinates, prove the duality principle and various famous theorems, among which those of Desargues, Pascal, Pappus, and so on. The theory of projective quadrics contains the essential notions of pole and polar hyperplane, with the notion of tangent as a sub-product. We also pay attention to the topological properties of the projective real spaces.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References and Further Reading
F. Borceux, An Axiomatic Approach to Geometry, Geometric Trilogy I (Springer, Berlin, 2014)
F. Borceux, A Differential Approach to Geometry, Geometric Trilogy III (Springer, Berlin, 2014)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Borceux, F. (2014). Projective Geometry. In: An Algebraic Approach to Geometry. Springer, Cham. https://doi.org/10.1007/978-3-319-01733-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-01733-4_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01732-7
Online ISBN: 978-3-319-01733-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)