Wednesday, May 4, 2011

Approximating Pi

In the ancient times, there was no direct way to find the area of a circle. Mathematicians approximate it by using inscribed polygons.  Since it is possible to find the area of any polygon by dividing it into triangles, it is also possible to approximate the area of a circle by increasing the number of sides of the inscribed polygon.

To illustrate this concept, consider the circle with radius 1 as shown below.  To increase the number of sides of the inscribed polygon, move slider n to the right. What do you observe?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

As n increases, the area of the inscribed polygon approaches the area of the circle (Can you see why?). Intuitively, as we increase n, the better our approximation. As shown above, the area of the circle is approximately equal to 3.14....  This number is now known as the irrational number pi.

To download the applet, click here, and then click File>Save on your browser. 

1 comment: