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Published in:
2011 | OriginalPaper | Chapter
7. Euclidean Motions of the Line, the Plane and of Space
Author : Agustí Reventós Tarrida
Published in: Affine Maps, Euclidean Motions and Quadrics
Publisher: Springer London
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Abstract
In this chapter we study Euclidean motions in dimension 1, 2 and 3. For instance, in dimension three there are only three types of Euclidean motions: helicoidals (that include rotations, translations and the identity), glide reflections (that include mirror symmetries) and anti-rotations.
The subsections are
7.1
Introduction
7.2
Classification of Euclidean motions of the line
7.3
Classification of Euclidean motions of the plane
7.4
Geometrical interpretation
7.5
Classification of Euclidean motions of the space
7.6
Geometrical interpretation
7.7
Composition of rotations in dimension three
Exercises