Euclidean Geometry

Francis Borceux
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Francis Borceux: Université catholique de Louvain

Chapter Chapter 4 in An Algebraic Approach to Geometry, 2014, pp 137-180 from Springer

Abstract: Abstract Affine real spaces can be provided with an additional “scalar product”, which yields corresponding notions of distance, angle, perpendicularity. And of course various additional geometric notions can now be studied: squares, rectangles, rotations, orthogonal projections, and so on. In particular, the theory of orthogonal projections provides many interesting applications in approximation problems: approximation by the law of least squares, Fourier approximation, and so on.

Keywords: Real Affine Space; Direct Isometries; Quadratic Euclidean; Orthogonal Symmetry; Inverse Isometry (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-01733-4_4

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