The CYCLOID is traced by a point on the circumference of a circle which ROLLS without slipping over a straight line.

1. What happens when the radius of the circle increases?[br]2. Does the shape of the cycloid change, or does it simply become bigger?[br]3. What happens if the tracing point begins somewhere other than the bottom of the wheel?[br]4. How many arches are produced after two complete rotations?[br]5. Where does the curve change direction?