Cutting Pi

None needed.

Carefully wrap the string around the circumference of your circular object. (You may want to ask a partner to help you.) Cut the string at exactly one circumference of your object (see photos below).

Take your “string circumference” and stretch it across the diameter of your circular object. Then cut as many “string diameters” from your “string circumference” as you can (as shown in the photo below).

How many string diameters could you cut from the string circumference? What do you notice?

Cutting string diameters from a string circumference is a physical way to divide the circumference of a circle by its diameter. No matter what circle you use, you’ll be able to cut three complete diameters and have a small piece of string left over.

What fraction of the diameter do you think this small piece could be? It should be about one-seventh. That means you’ve cut about 3 and 1/7 pieces of string, which is the value of pi—the ratio of a circle’s circumference to its diameter.