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.

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.

This Science Snack is part of a collection that showcases female mathematicians and math educators whose work aids or expands our understanding of the phenomena explored in each Snack.

Mary Laycock was one of the foremost mathematics educators of the 20th century and wrote hundreds of articles and books about teaching mathematics. Mary pioneered the teaching of hands-on mathematics and discovery learning, making mathematics more accessible to all students. “Mary’s Math” shows up in our Pi Day Science Snacks activities, and she consulted on the creation of this exhibit! She said, “You know what I call kids who get all the right answers? Lucky!” In this Science Snack, based on one of Mary's activities, you get to measure pi in fun and creative ways.