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?

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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. 

Circle Approximation Graph

1.) Move slider r below to adjust the radius of the circle.
2.) Move slider n and observe what happens.
3.) Make a conjecture about your observations


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The area of a circle can be approximated by inscribing and circumscribing a polygon with n sides. As the number of sides of the inscribed/circumscribed polygon increases, their areas approach the area of the circle.