Abstract
This chapter discusses real Euclidean space. The concept of a Euclidean space encompasses Euclidean plane and the three-dimensional space of Euclidean geometry as spaces of dimensions 2 and 3, respectively. The term Euclidean distinguishes these spaces from other types of spaces considered in modern geometry. Euclidean spaces also generalize to higher dimensions. From the modern viewpoint, there is essentially only one Euclidean space of each dimension. With Cartesian coordinates, it is modeled by the real coordinate space (Rn) of the same dimension. In dimension one, this is the real line; in dimension two, it is the Cartesian plane; and in higher dimensions, it is a coordinate space with three or more real number coordinates.
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