Since we live in a 3 dimensional world, many problems we encounter in fields such as science and engineering, as well as others, are modelled mathematically using 3 variables, hence, 3D.

The first coordinate system introduced to students to handle 3 variables is an extension of the 2D Cartesian coordinate system. If another number line is added to the 2D system that is 90° t0 the previous 2 axes, with the origin coinciding with the other two origins, you have the 3D system. The third axis is called the *z*-axis. So a point now needs 3 numbers to place it in 3D space: (*x*,*y*,*z*). Frequently, to draw a 3D grid on a 2D surface, the *y* and *z* axes are drawn in he plane of the surface and the *x* axis is drawn in perspective to show that it is perpendicular to the surface. So placing a point in a 3D Cartesian frame is an artistic challenge for me but drawing dashed lines parallel to the axes helps:

There are other orientations of the 3 axes when showing them in 2D, but this is a very common one.

As with the 2D Cartesian coordinate system, equations relating the variables *x*, *y*, and *z* can be plotted, showing all the values of *x*, *y*, and *z* that make the equation true.

In 2D, a general equation of a line is *ax* + *by* = *c*, where the *a*, *b*, and *c* are specific numbers. For example, the set of points that satisfy the equation 2*x* -3*y* = 7, plot as a straight line. By extension, in 3D, the general linear equation is *ax* + *by* + *cz* = *d*. Though this is called a *linear* equation, it plots as a plane in 3D:

The 3D version of a circle in 2D is a sphere. The generic equation of a sphere of radius *r* centred at the origin is *x*^{2} + *y*^{2}+ *x*^{2} = *r*^{2}:

Very interesting shapes can be made using 3D graphs. Here are a few:

As with 2D, there are other ways of locating points in 3D. I will present some of these in my next post.