Projective Geometry

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 6 in An Algebraic Approach to Geometry, 2014, pp 195-265 from Springer

Abstract: 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.

Keywords: Projective Quadrics; Desargues; Duality Principle; Pappus; Polar Hyperplane (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01733-4_6

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DOI: 10.1007/978-3-319-01733-4_6

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