Greenwood press

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PERIMETER
The outdoor running track at the Rock
Norman Complex, Clemson University,
contains two semicircles and two sides
that are each 100 meters in length. The
turns require precision marking to
ensure that all athletes run the same
distance in a race.

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PERIODIC FUNCTIONS
Graphs of functions that repeat shapes are called periodic. The horizontal
length of each repetition is called the period. Phenomena that are based on cir-
cular motion, such as the rotation of the earth around the sun, will often result in
a periodic graph. The graph below shows the hours of daylight on the fifteenth
of each month for Minneapolis. The data points start with January 15th and are
plotted for two years. The period for this graph is 1 year, or 12 months. The curve
that has been used to approximate the data points is a sine curve, where 
x is the 
month number: Hours 
= 12.2 + 2.9 sin((x − 2.3) •
2π
12
).
The tilt of the earth and its rotation about the sun cause the sinusoidal pattern
in hours of daylight. Because temperature in a city is dependent on hours of sun-
shine, plots of the average monthly temperature of American cities will be in the
form of a sine curve.
Circular motion can arise from a variety of sources. The distance above
ground of a passenger in a Ferris wheel produces a sine curve as the wheel
rotates. Measures on a pendulum will produce periodic functions. Gravitational
attraction to the moon causes tides. As the moon rotates about the earth, the
heights of tides will produce a periodic function.
Sound, radar, light, radio, and ocean waves are periodic. When you press
middle A on a piano, the piano strings vibrate, producing sound waves that have
a period of 1/440 second. An oscilloscope provides a video screen for viewing
different electrical patterns. An EKG machine in a hospital is an oscilloscope for
viewing the periodic electrical patterns from a patient’s heart.