Students will use trigonometric ratios to discover the circumference of regular polygons inscribed within and circumscribed about a circle. These ratios will help approximate a value of pi.
Before the Activity
I read the book "The Greedy Triangle" by Marilyn Burns.
During the Activity
To start the activity, a 30-60-90 triangle should be drawn with the hypotenuse from the center of the circle to a vertex of the triangle. Define the angle theta as the central angle of the circle. The students should see a pattern after drawing out the equilateral triangle and square.
After the Activity
Question #9 on the worksheet leads into a great discussion of limits.