Rigid Motions (Isometries)

Abstract

Section 2.1 discusses the vectors and their use in analytic geometry. In Section 2.2 we study rigid motions of ${\mathbb{R}}^{n}$ (n≥2), including the complex and quaternionic approaches. Section 2.3 is devoted to the geometry on a sphere (induced by Euclidean geometry of the space), it and also introduces the stereographic projection. The study of polyhedra is organized in Section 2.4 in into the a sequence of themes: the notion of a polyhedron, Platonic solids, symmetries of geometrical figures, star-shaped polyhedra, and Archimedean solids. Section 2.5 (Appendix) surveys matrices and groups.