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Euclidean Motions of the Line, the Plane and of Space

  • Agustí Reventós Tarrida
Part of the Springer Undergraduate Mathematics Series book series (SUMS)

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
  1. 7.1

    Introduction

     
  2. 7.2

    Classification of Euclidean motions of the line

     
  3. 7.3

    Classification of Euclidean motions of the plane

     
  4. 7.4

    Geometrical interpretation

     
  5. 7.5

    Classification of Euclidean motions of the space

     
  6. 7.6

    Geometrical interpretation

     
  7. 7.7

    Composition of rotations in dimension three

     
  8. Exercises

     

Keywords

Orthonormal Basis Axial Symmetry Characteristic Polynomial Canonical Basis Central Symmetry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain

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