This demo includes one graphical display window that shows the curve X(t) and the point X(t0).

The control window displays the arclength L of X(t), the area A enclosed by X(t) if X(t) is a simple curve, and the ratio L2/4piA, which is always greater than or equal to 1 according to the isoperimetric inequality.

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.