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Projective Geometry: A Short Introduction

Projective geometry : A Short IntroductionLecture NotesEdmond BoyerMaster MOSIGI ntroduction to Projective GeometryContents1 Objective .. Historical Background .. Bibliography ..42 Projective Definitions .. Properties .. The hyperplane at infinity .. 123 The Projective Introduction .. Projective transformation ofP1.. The cross-ratio .. 144 The Projective Points and lines .. Line at infinity .. Homographies .. Conics .. Affine transformations .. Euclidean transformations .. Particular transformations.

Master MOSIG Introduction to Projective Geometry A B C A B C R R R Figure 2.2: The projective space associated to R3 is called the projective plane P2. De nition 2.2 (Algebraic De nition) A point of a real projective space Pn is represented by a vector of real coordinates X = [x

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