Cutting Pi

String and scissors are all you need to find pi all around you.

It may be hard to cut pie into equal pieces, but in this Snack, you can cut string into pi pieces!

Subjects:

Keywords:

pi

patterns

constant

video

Video Demonstration

Tools and Materials

Circular or cylindrical object, such as a straight-sided coffee cup, roll of tape, plate—or even a pie
String
Scissors
Optional: partner

Assembly

None needed.

To Do and Notice

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?

What's Going On?

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.

Going Further

Doing this Snack is a great way to celebrate Pi Day, which happens on March 14 every year. Pi Day was founded at the Exploratorium by Larry Shaw in 1988. Find out more about how you can celebrate it here.

Related Snacks

Science activity to estimate pi with the random tossing of toothpicks