# Perimeter and Circumference

Hello. My name is Vickie Vickery and I have been a Middle and High
School Math teacher for 14 years. Today's lesson will be useful to
students taking Math in the 7th and 8th grade. On the following pages
students will learn how to find the perimeter of polygons and the
circumference of circles.

## Circumference

In our lesson, we want to find the distance around a circle. But
we do not call it perimeter but circumference. A circle is not a
polygon, but a closed curve in the plane which begins and ends at the
same point. Every point on the closed curve is the same distance
from the a fixed point within. Measuring the circumference of a
circle, however is more difficult than measuring the perimeter of a
polygon. It is easy to measure the diameter of a circle which is the
line segment that goes through the center of a circle with both
endpoints on the circle. It has been proven that the
circumference of a circle is about 3 1/7 times
the diameter of the circle. This fact can be shown by measuring the
diameter of a circle with a string and carefully place the string on
the circle. Now see how many times does the length of the diameter go
around the circle. As you may have found, it takes three
diameters with a little bit left over no matter how large or small
the circle.

This relationship is so important that it is represented by the
Greek letter p [pie]
spelled pi. The fraction 3 1/7 and the decimal
3.14 are the most often used approximations of
p;
however, a more exact, but still approximate value of
p is 3.14159. Pi is an
irrational number, and therefore has a nonterminating, nonrepeating
decimal representation.

If we multiply the diameter d by p,
we can find the circumference of the circle. Therefore we use
the formula C = pd where C =
circumference, p = 3.14 or 3
1/7, and d = diameter.

Since it takes two radii to make a diameter, we can substitute 2r,
where r = radius, for the d (diameter) in the formula to make a new
formula when the radius is given: C = 2rp
or as it is usually written C = 2pr.

Remember always to record the unit of measure with your answer for
the perimeter and circumference.

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Go to Links Page.

The views expressed on this page are not necessarily those of the
University of South Carolina.
http://rpsec.usca.sc.edu/Classwork/731sp2000/Lesson/VickeryL/Vick2.htm
(March, 2000)