Euclidean Motions of the Line, the Plane and of Space

Part of the Springer Undergraduate Mathematics Series book series (SUMS)


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


  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



Orthonormal Basis Axial Symmetry Characteristic Polynomial Canonical Basis Central Symmetry 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

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

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