Students will approximate pi by setting up trigonometric ratios and calculating the areas of regular polygons inscribed within and circumscribed about a circle.
Before the Activity
I use the "Approximation of Pi Using Archimedes' Method" activity first. This activity follows the same format. After doing the first activity, the students can usually do this activity rather quickly.
During the Activity
Have the students draw a 30-60-90 triangle in the first diagram, with the hypotenuse extending from the center of the circle to a vertex of the triangle. Define an angle theta as a central angle of the circle.
After the Activity
Question #8 leads into a great introduction of limits.
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