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
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7.1
Introduction
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7.2
Classification of Euclidean motions of the line
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7.3
Classification of Euclidean motions of the plane
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7.4
Geometrical interpretation
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7.5
Classification of Euclidean motions of the space
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7.6
Geometrical interpretation
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7.7
Composition of rotations in dimension three
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Exercises
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© 2011 Springer-Verlag London Limited
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Reventós Tarrida, A. (2011). Euclidean Motions of the Line, the Plane and of Space. In: Affine Maps, Euclidean Motions and Quadrics. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-0-85729-710-5_7
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DOI: https://doi.org/10.1007/978-0-85729-710-5_7
Publisher Name: Springer, London
Print ISBN: 978-0-85729-709-9
Online ISBN: 978-0-85729-710-5
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