Clifford Algebra in Flat n-Space

Abstract

The word “geometry”is derived from a greek word meaning “to measure land.”The starting point for differential geometry is the definition of an infinitesimal distance. Generally, such an infinitesimal distance ds is defined in terms of a coordinate system. For the Cartesian coordinate system applied to an n-dimensional Euclidean space, we have

$${(\mathrm{d}s)}^{2} ={ \sum \nolimits }_{j=1}^{n}{(\mathrm{d}{x}^{j})}^{2}.$$

(4.1)