The epicycloid from Exercise Sheet 1
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The following picture shows the epicycloid of Exercise Sheet 1. The radius of the circle centred at \(O\) is fixed, and the radius of the outer circle is \(r\) (which you can change by clicking and dragging the endpoints of the interval labelled \(r\) in the diagram).
You can click and drag the point \(B\) to change the angle \(\alpha\). The point \(C\) on the outer circle will follow, so that the arclength from \(B\) to \(A\) equals the arclength from \(B\) to \(C\). Equivalently, imagine that the outer circle rolls without slipping around the outside of the inner circle.
The point \(C\) then moves along the green curve, which is the epicycloid associated to these two circles.
