Non—Euclidean Geometry

Computing the distance between points on a plane is a trivial matter once we erect a Cartesian coordinate system on it—we simply use equation (7.1). Seen from a three—dimensional vantage point, the plane may have any position or orientation we like. If we choose to remain “in” the plane, we can regard it as a two—dimensional space in its own right: the possibility of erecting Cartesian coordinates upon it, and using equation (7.1) to measure distances between its points, characterizes it as a “flat” or Euclidean space.