Titlebook: Affine Maps, Euclidean Motions and Quadrics; Agustí Reventós Tarrida Textbook 2011 Springer-Verlag London Limited 2011 affine geometry.bil

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Affine Spaces,rm with points and straight lines is the triangle. In this chapter we shall see two important results that refer to triangles and the incidence relation: the theorems of Menelaus and Ceva..In the Exercises at the end of the chapter we verify Axioms 1, 2 and 3 of Affine Geometry given in the Introduction..The subsections are

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Orthogonal Classification of Quadrics, definition of . among various real numbers. Most textbooks are not concerned with the faithfulness of this list: that is, that each quadric appears in the list once and only once; for this reason this concept of good order is, as far as we know, new in this context..We also study the symmetries of a given quadric. The subsections are

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Affinities, we shall see that affinities are simply those maps that take collinear points to collinear points..We shall also see that there are enough affine maps. In fact, in an affine space of dimension ., given two subsets of .+1 points, there exists an affine map such that takes the points of the first sub

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Textbook 2011en-for-granted, knowledge and presents it in a new, comprehensive form. Standard and non-standard examples are demonstrated throughout and an appendix provides the reader with a summary of advanced linear algebra facts for quick reference to the text. All factors combined, this is a self-contained b