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Pi Graph

Science Snack
Pi Graph
Use straight lines to learn about circles.
Pi Graph
Use straight lines to learn about circles.

Graphing data can help you discover patterns in nature. This Snack reveals an important ratio found in circles.

Tools and Materials
  • Cylindrical or circular objects of different sizes, such as plates, poster tubes, rolls of tape, or bottle caps
  • String
  • Metric ruler
  • Paper and pencil (not shown)
  • Graph paper
  • Optional: several partners and a large piece of graph paper to collect group data

None needed.

To Do and Notice

On a piece of paper, create a chart like the one below. Measure the diameter of each object and record it on the chart. Then—using a piece of string wrapped around the object—measure the circumference, and record it on the chart.

           Object                     Diameter (cm)      Circumference (cm)


On your graph paper, plot the points that represent each object, where the x coordinate is the diameter and the y coordinate is the circumference. (If you’re doing this with other people, you might want to combine all your data points on a large piece of graph paper.)

Draw a best-fit straight line that goes through the points. Not all points will touch, but you can estimate the line in space that the points seem to best cluster around.

Calculate the slope of the line by choosing a point on the line and dividing the y coordinate by the x coordinate.

What's Going On?

In this Snack, the points you plot for different circles or cylinders should form a straight line, which indicates that there’s something constant in the linear relationship between any circle’s diameter and circumference.

This constant of proportionality is called the slope of the line. When you divided the y coordinate (circumference) by the x coordinate (diameter), you should have found something close to the value of pi, one of the most important mathematical constants.

Pi, which is defined by the ratio of a circle’s circumference to its diameter and expressed with the Greek symbol π, is approximately 3.14. This relationship is often represented as the formula for a circle’s circumference: c = π*d.

Going Further

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.

Highlighted Scientist: Dr. Emma Haruka Iwao

Source: Wikimedia Commons

Emma Haruka Iwao (pictured above) is a mathematician and computer scientist who broke the Guinness world record for calculating the most digits of pi in 2019, and held that record until 2020. Fascinated with pi since childhood, she calculated pi on her computer when she was 12 years old! Inspired by her own fascination with pi, Iwao and a Google team computed pi to 31.4 trillion decimal places (3.14 x 1013), far more digits than the previous record. Two others (one individual and one team) beat her 2019 record, and she regained the record in 2022, calculating 100 trillion digits of pi! Explore the mathematical constant pi with our Pi Graph Science Snack.