There are many ways to describe a surface. Consider the following descriptions:

• the unit sphere;
• $x^2+y^2+z^2=1$;
• $r=1$ (where $r$ is the spherical radial coordinate);
• $x=\sin\theta\cos\phi$, $y=\sin\theta\sin\phi$, $z=\cos\theta$;
• $\rr(\theta,\phi) = \sin\theta\cos\phi\,\xhat + \sin\theta\sin\phi\,\yhat + \cos\theta\,\zhat$;

all of which describe the same surface. Here are some more ways of describing surfaces: (Are these descriptions of the unit sphere?)

• The graph of $z=x^2+y^2$;
• The figure shown at the right.

Which representation is best for a given problem depends on the circumstances. Often you will have to go back and forth between several representations.