Example 1.23.  Show that the circle C with center and radius can be parameterized to form a simple closed curve.

Solution.  Note that the required parametrization is

              

    Figure 1.23 shows that, as t varies from , the circle is traversed counterclockwise.  If you were traveling around the circle in this manner, its interior would be on your left.  When a simple closed curve is parametrized in this fashion, we say that the curve has a positive orientation.  We will have more to say about this idea shortly.

Explore Solution 1.23.

Enter    and construct the standard parameterization for the circle.
Use the complex exponential form .  

(c) 2006 John H. Mathews, Russell W. Howell