Calculating Pi

The circumference of a circle is the distance around a circle. The diameter is the distance across the circle that passes through its center.

For any circle, regardless of diameter, there is a consistent ratio between the circle’s circumference and the length of its diameter.

Watch this video to observe a mathematician’s exploration of this ratio, which he calls "pi."

For an extended version with a more detailed discussion about diameter and pie watch the video below. The video is filmed in the United Kingdom, so you will hear him referring to "football" which in the United States of America we call soccer.

Exploring Ratios with Circumference

The circumference of a circle is the distance around the outside of the circle. The diameter is the distance across the circle. It must pass through the center or the circle.

For any circle, regardless of diameter, there is a consistent ratio between the circle’s circumference and the length of its diameter.

The radius is the distance from a circle’s center to a point on the circle. There is also a consistent ratio between the circle’s circumference and the length of its radius.

Select the Investigation Menu to explore these ratios.

• Collect data points by dragging the radius to various lengths by clicking on the square that highlights a point on the circle.
• Click the "Add to Table" button to record the data in the table. By default, the radius, diameter, circumference and area are shown in a table.
• Click on the x/y button to identify the ratio you would like to see represented.
• Click on the graph button to graph the data.

After you have explored the measures of five or six circles, answer the following in your math journal:

1. What is the ratio of a circle’s circumference to its diameter?
2. What is the ratio of a circle’s circumference to its radius?
3. What is the relationship between these two ratios? How is this relationship connected to the relationship between the radius and the diameter of a circle?