Parametrization side-by-side

The example below gives a parametric curve (or a parametrization) in two-dimensional space. While you can change the parametrization (try it!), the default has and with the parameter going from to . There are two views. First, in the left view, you see the horizontal axis is the t-axis. The curve in red gives x(t) while the curve in blue gives y(t). The view on the right shows the parametric curve in black. It is best to imagine a parametric curve in the following way: imagine that a bug travels along the path of the "loopy" black curve given in the view on the right. In fact, at one moment in time, the bug is located at the purple point. On paper, people usually indicate the direction the bug is traveling by drawing an arrow on the curve. All of the color coding (red vs. blue vs. purple) is all intentional. If you want to have the app not do the animations for you, then use your mouse to adjust the purple slider for the value of t yourself. (You can always reload the app).