Euclidean Motions of the Line, the Plane and of Space
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.
Classification of Euclidean motions of the line
Classification of Euclidean motions of the plane
Classification of Euclidean motions of the space
Composition of rotations in dimension three