Affine Geometry

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 2 in An Algebraic Approach to Geometry, 2014, pp 51-118 from Springer

Abstract: 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.

Keywords: Affine Geometry; Arbitrary Field; Affine Space; Supplementary Subspace; Subspace Parallel (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-01733-4_2

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