1. Title: Computing Pi
Purpose: The general purpose of this applet is to see how pi is calculated using polygons and a circle. The circle is inscribed and circumscribed by polygons , students have the opportunity to vary the number of sides of each polygon and see how that affects the relationship to the circle.
Target Audience: Students from 6th - 12th grade. (However, I learned this exact method in college during my study of limits.)
2. This applet gives a brief description of the history of pi and how it was approximated by Archimedes. The instructions are quite simple in that all the student has to do is move the bar to the left and right to change the number of sides of each inscribed and circumscribed polygons. Two images show the area and the circumference of each circle and how the number of sides of the polygon increase approaches pi. The blue numbers represent the area and circumference of the circle and the red numbers represent the area and circumference of the polygons. Asthe student changes the number of sides, they can see that the larger the number of sides of a polygon the area and circumference of a circle reach the same value which is pi. I think that this model works spectacularly well because it makes it much easier to see the effects of changing the number of sides of each polygon, versus having to always draw and redraw each polygon. This applet is very easy to use and portrays a lot of information with very little movement at all. All the student needs to recognize is the kind of pattern that emerges as they manipulate the variables. If the student needs some kind of direction to help their thinking process, the down tab for the "Exploration" gives students questions to consider as they play around with the model.