Many familiar things go through cycles:

• The sun (and the moon) rise and fall regularly each day.
• The seasons repeat regularly every year.
• Tides come in and go out at regular intervals.

Some of these kinds of events are measurable, and we can create functions to model and study them. For example, imagine that there is a spot of paint on a bike tire with a 26-inch diameter. We can measure the height of the spot above the ground as the bike moves. Here is what a table and graph of the relationship between the distance the bike has traveled and the height of the spot would look like:

distance bike travels (inches)	height of paint spot (inches)
0	0
10	3.66
20	12.58
30	21.74
40	25.97
50	22.90
60	14.26
70	4.90
80	0.11
90	2.57
100	10.91

We can make some observations about the situation using the graph. For example, the height of the paint spot will never be less than 0 or greater than 26. This makes sense for the situation since the tire will not go below ground, and it can reach only 26 inches (the wheel’s diameter) above the ground. The height of the paint spot will go up and down in a repeating pattern as the tire rotates. This kind of function is called a periodic function because it represents something that happens over a certain interval and then repeats.