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.
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References and Further Reading
F. Borceux, An Axiomatic Approach to Geometry, Geometric Trilogy I (Springer, Berlin, 2014)
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© 2014 Springer International Publishing Switzerland
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Borceux, F. (2014). Euclidean Geometry. In: An Algebraic Approach to Geometry. Springer, Cham. https://doi.org/10.1007/978-3-319-01733-4_4
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DOI: https://doi.org/10.1007/978-3-319-01733-4_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01732-7
Online ISBN: 978-3-319-01733-4
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