This demo displays the epicycloid given by X(t) = ((a + b)cos(t) – bcos(((a + b)/b)t), (a + b)sin(t) - bsin(((a + b)/b)t)). To change the variables a, b, and t0, use the following keys on the appropriate line in the control window:

[<]: Decrease variable by one step.
[>]: Increase variable by one step.
[<<]: Decrease variable until it reaches its minimum value.
[>>]: Increase variable until it reaches its maximum value.

By default, the demo shows the point tracing out the curve, so that only part of it is shown. To show the entire curve, check the box "Show entire curve" by clicking on it. Click on the "Show position vector X(t0)" box to show the position vector X(t0) whose components are the coordinates of the point X(t0).