This demo includes two graphical display windows.

The window "Curve: X(t)" displays the curve X(t) and the point X(t_{0}).

The window "kg(t)" shows a graph of kg(t) and the point (t_{0},
k_{g}(t_{0})).
Note that, as stated in the Four-Vertex Theorem, there are always at
least four critical points of k_{g}(t).

You can change t_{0} 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.