|28||Beyond Three Dimensions|
As you have seen, the rectangular (also called the Cartesian, after the French mathematician René Descartes) coordinate plane is defined by two number lines that intersect at a right angle. Cartesian three-space or xyz space is defined by three number lines that intersect at a single point, such that each line is perpendicular to the plane determined by the other two lines. What about Cartesian four-space? Or five-space? Or infinityspace? These can exist too, but they’re difficult to visualize.
A system of rectangular coordinates in four dimensions—Cartesian four-space—is defined by four number lines that intersect at a single point. That point, the origin, corresponds to the 0 point on each line. ...