A question about a rolling circle.

This was created in reply to a question from LinkedIn, asking as to the number of rotations of a circle of radius 1 as it rolls around a circle of radius 4. In this case the point that starts out at the bottom of the small circle is indicated each time it returns to the bottom of that circle. The red path can be graphed on any graphic calculator provided correct parametric equations can be identified.

Information: A question about a rolling circle.