A Circumference Investigation

What is the relationship between a circle's circumference and it's diameter? The circle below has a given diameter of 2 units. We do not know the circumference, but we can approximate it using an inscribed regular polygon.

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1. Using the red slider to adjust the drawing, record the perimeter of the regular polygons with the following number of sides: 3, 4, 5, 6, 10, 20, 50, and 100. Create a two-column table of values for this data.

2. Describe what happens to the perimeter values as you increase the number of polygon sides in your own words.

3. Predict the perimeter of a regular polygon with 200 sides and 2000 sides. Why did you choose the values you wrote?

4. Now adjust the green slider so that you have a diameter value of 1 unit and record the perimeters for the regular polygons with same side numbers used before: 3, 4, 5, 6, 10, 20, 50, and 100.

5. Have you seen the perimeter value for the 100-sided polygon before? If so, what do you think it is?

6. Describe the relationship (if any) between the perimeter values found in questions 1 and 4.

Michael C. Powell, Created with GeoGebra