Geometry pp 7-42 | Cite as

Affine Geometry

  • Michèle Audin
Part of the Universitext book series (UTX)


An affine space is a set of points; it contains lines, etc. and affine geometry(1) deals, for instance, with the relations between these points and these lines (collinear points, parallel or concurrent lines…). To define these objects and describe their relations, one can:
  • Either state a list of axioms, describing incidence properties, like “through two points passes a unique line”. This is the way followed by Euclid (and more recently by Hilbert). Even if the process and a fortiori the axioms themselves are not explicitly stated, this is the way used in secondary schools.

  • Or decide that the essential thing is that two points define a vector and define everything starting from linear algebra, namely from the axioms defining the vector spaces.


Vector Space Convex Subset Affine Transformation Vector Subspace Affine Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Michèle Audin
    • 1
  1. 1.IRMAUniversité Louis PasteurStrasbourgFrance

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