This demo includes two graphical display windows.

The window "Curve: X(t)" displays the curve X(t) and the point X(t0).

The window "kg(t)" shows a graph of kg(t) and the point (t0, kg(t0)). Note that, as stated in the Four-Vertex Theorem, there are always at least four critical points of kg(t).

You can change t0 and X(t) in the control window. The control window also includes a list of curves that you can enter for X(t) and parameters used in defining those curves. For example, enter cardioid(t) in the X(t) textbox to make X(t) a cardioid. Changing k will then change the cardioid.