Euclidean (also seen as Euclidian) space is often called Cartesian space, or more simply, n-space. It is made up of n dimensions and is a set of points, with each point represented by a coordinate of n components. Space with two to three dimensions—and that does not use Einstein’s and others’ ideas of relativistic physics—are considered Euclidean space.

In Euclidean space, distance is defined by certain “rules”: The distance between two points is positive, unless they are the same points; the distance from points a to b will be the same as from b to a; and the distance between the points does not change if they are totally shifted over in one direction (such a sliding over of the points is called translation; for more on this, see elsewhere in this chapter). In addition, the Pythagorean theorem is valid for three points that are the vertices (the intersection points of the sides of an angle) of a right triangle.