Projective Geometry

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 6 in An Axiomatic Approach to Geometry, 2014, pp 197-241 from Springer

Abstract: Abstract The attempts to formalize the rules of perspective representation lead the mathematicians of the seventeenth century to consider seriously “points at infinity”. This is the birth of projective geometry which, in a first approach, proves to often unify in a single statement various bunches of similar Euclidean results. The study of conics and polar lines leads to the recognition of the duality principle in projective geometry. During the nineteenth century, an elegant system of axioms for projective geometry is individualized and the close connection with projective spaces over a field is established.

Keywords: Projective Plane; Projective Geometry; Euclidean Plane; Central Projection; Perspective Representation (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-01730-3_6

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