Students will use the diameter of a circle and the perimeter of various polygons to estimate and discover the value of pi.
There are three main values you are going to focus on in this activity: 1) The slider, which represents the number of sides of your polygon. 2) The distance of one of the sides of the regular polygon, line segment CB. 3) The diameter of the circle that circumscribes the polygon, line segment EB. If the polygon gets too large to see the values, look at the table on the left. TASK: 1) Calculate the perimeter of the triangle. You can do this by multiplying the distance of line segment CB by the number of sides. 2) Divide the perimeter by the diameter of the circle. 3) Write this value in a table with number of sides in the first column and ratio of perimeter to diameter in the second column. Repeat steps 1 and 2 for polygons with 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100 sides by moving the slider to the appropriate number of sides. Add to the table of values. 3) What do you notice about the polygon as the number of sides increases? 4) What do you notice about the relationship between the perimeter of the polygons and the diameter of the circle?