Measuring Circles

Objective. The objective of this lesson is for you to measure many circles to try to discover if there is a special relationship between their circumference and their diameter.

A circle's circumference or perimeter is the distance around the circle. This is shown in red in the figure below. Starting at point A, going all around the circle, and ending on the same point A represents the circumference of the circle:

The diameter is the longest line segment that you can have inside a circle. These line segments go through the center of the circle and have their endpoints on the circle. The previous picture shows three examples of diameters in green, yellow, and brown.

Now that you know what circumference and diameter are, here are a few questions for you.

  1. Think of many circles of different sizes. Do you think there is a relationship between the circumference and the diameter?
  2. If so, what might the relationship be?
  3. Looking at the figure above, how many times larger do you think the circumference is than its diameter? Try to estimate a number.
Make sure to answer the questions above before continuing.

Doing the measurements. At the bottom of this page you will find an applet (see note 1) that you will use to make many circles and measure their circumference and diameter. You should do about 10 circles with diameters that vary between 10 and 150 units (see note 2). Make sure to try a circle with a diameter of 70 units. When measuring the circumference, make sure that the starting point (where the small line in the circle is) goes around a complete cycle until it ends as close to the center and as close to vertical as possible.

You need to record both measured quantities in a table. You can do this table in three different ways:

  1. On a piece of paper,
  2. Using a spread sheet program in your computer, like excel, or
  3. Using the table provided with this lesson.
If you decide to use paper, look at the table provided to see the format that you should use.
IMPORTANT NOTE: If you choose to use the table provided, be aware that if you exit from that page you will loose all the results. You can certainly fill it in and print it, but as soon as you exit from it, the data is gone. You need to leave the table page open as you go to the next page of this lesson because you will need it there.

Now go ahead and click on the ? symbol in the applet to read the instructions on how to use it, measure both dimensions for 10 circles, and fill out the first two columns of the table. When done, go on to the next page to analyze the data.

If your browser recognized the applet tag, you would see an applet here.

 


Preface


Table of Contents


Analyzing the Data

 

[Note 1] -- A Java applet is simply a computer program written in the Java computer language. One of the good features of a program written in Java is that it can be downloaded from the web and run on almost any computer.

[Note 2] -- We use what we call units for the dimensions because when working with online figures centimeters or inches don't really make sense on the screen. However, the concept is exactly the same.

Last Updated: Monday, 12-Aug-2002 02:25:24 GMT

 


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