Abstract
In affine geometry it is possible to deal with ratios of vectors and barycenters of points, but there is no way to express the notion of length of a line segment or to talk about orthogonality of vectors. A Euclidean structure allows us to deal with metric notions such as orthogonality and length (or distance).
Rein n’est beau que le vrai.
—Hermann Minkowski
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© 2001 Springer Science+Business Media New York
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Gallier, J. (2001). Basics of Euclidean Geometry. In: Geometric Methods and Applications. Texts in Applied Mathematics, vol 38. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0137-0_6
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DOI: https://doi.org/10.1007/978-1-4613-0137-0_6
Publisher Name: Springer, New York, NY
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