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Affine Geometry

In: An Algebraic Approach to Geometry

Author

Listed:
  • Francis Borceux

    (Université catholique de Louvain)

Abstract

The development of abstract algebra during the 19th century allows using structural algebraic arguments instead of calculations in terms of coordinates. It allows also developing geometry over an arbitrary field of coordinates, not just the reals or the complexes. Affine geometry is classically devoted to the study of all geometric properties valid over an arbitrary field; this contains in particular the theory of parallelism, translations, projections, symmetries, conics, quadrics, and so on.

Suggested Citation

  • Francis Borceux, 2014. "Affine Geometry," Springer Books, in: An Algebraic Approach to Geometry, edition 127, chapter 0, pages 51-118, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-01733-4_2
    DOI: 10.1007/978-3-319-01733-4_2
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