For each object, estimate the circumference. Then measure the circumference and the diameter in centimeters to the nearest tenth (e.g., millimeters). Use string or a tape measure. Record your data in the table.
Examine the table. What do you notice about the ratio of C to d? Based on these data, what is the relationship between the diameter and circumference of a circle?
Enter the values from the table for diameter and circumference into a graphing program in your computer or into a table in your graphing calculator to make a scatter plot. Use the horizontal axis (x) for diameter and the vertical axis (y) for circumference. Graph the points. What patterns do you see in the graphical data?
What information does a graph of these data provide? Note 5
A straight line indicates that the data are increasing by a constant amount. What is the constant in this case? Close Tip
Find the mean of the data in the C/d column. Why find the mean? Does the mean approximate ?
A mean is an average, or a sum of all the data values divided by the total number of data values. Note 7Close Tip
By now you have seen that all circles have one trait in common: The ratio of circumference to diameter is a constant value, , which is a little more than 3. Pi is an irrational number that is represented by the symbol . Note 6 Its decimal part continues forever without repeating. As of 1997, had been extended to 51 billion decimal places (using a computer)! Your calculator has a special key for , but this is only an approximate value.
Video Segment In this video segment, participants investigate the relationship of circumference and diameter using different circular objects. They collect the data by measuring, and then make observations about their findings.
Were you surprised to find out that , which is an irrational number, can be expressed as a constant ratio of two numbers, namely the diameter and circumference of any circle?
If you are using a VCR, you can find this segment on the session video approximately 9 minutes and 16 seconds after the Annenberg Media logo.