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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 .. Transformation hierarchy .. 25 Grenoble Universities1 Master MOSIGI ntroduction to Projective GeometryChapter ObjectiveThe objective of this course is to give basic notions and intuitions onprojectivegeometry.

around 600 BC: The familiar form of geometry begins in Greece. First abstract notions appear, especially the notion of in nite space. 300 BC: Euclide, in the book Elements, introduces an axiomatic ap-proach to geometry. From axioms, grounded on evidences or the experi-ence, one can infer theorems. The Euclidean geometry is based on mea-

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