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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)