A cycle is a series of repeating events; there are many mathematical curves which exhibit this behaviour. Thus a particular section of the graph of such a curve can be seen as a pattern which is then repeated many times. For example, a cycloid is the curve formed by the vertical position of a point on a circle which is rolling on a flat surface. There are a number of interesting facts about a cycloid, such as the fact that the area under the curve is three times the area of the circle which generates it. Also the length of the cycloid is four times the diameter of the generating circle. An example of a repeating cycloid is shown in Figure 6.1.