Q&A #864

Pi and the area of a circle

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From: Marielouise (for Teacher2Teacher Service)
Date: Dec 01, 1998 at 19:56:46
Subject: Re: area of a circle. Pi

Gail's method provides a good approximation for the area of the circle. The
more sections the circle is cut into the more accurate the answer.

Another way to approach this is to take a piece of 1/4 in graph paper. Open a
compass to to a reasonable distance, such as 10 squares and draw a circle
using one vertex of a small square as the center. Then use the radius of the
circle to build a square. If you used 10 squares the area of the square is 10
* 10.  Count the number of squares that are inside the circle as well as in
the square. You will have to approximate because along the edge you will be
getting only parts of the little squares. You could count number of squares
immediately outside and those immediately inside. Find the average of the
difference and add this average to the number of squares fully inside the
circle. You will get somewhere from 75-80 squares. Compare this number to
100.  Take this fractional part of 100 and multiply by four since there are
four quarters to the circle.

Four times the fraction is approximately Pi. 100 is 10^10 or radius^2.

-Marielouise, for the Teacher2Teacher service

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