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Areas as Limits

Dawn Lodewegen
Ledocq

Areas as Limits
In 250 B.C., Archimedes derived the formula for the area of a circle. We were instructed to find the formula of the area of a circle using the same method that Archimedes did. Everyone should be familiar with the formula giving the area of a circle as a function of it’s radius: A = pr2. We were instructed to look at the combined areas of inscribed triangles, and increase the number of triangles until we get closer and closer to the actual area of a circle.
In order to carry out the instructions above we must first determine the area of one of the inscribed congruent triangles in terms of the radius and some appropriate angle.


In this figure, the angle q = p/4 radians. If one is to put it into a general form
q = 2p/n, where 2p is the distance around the circle and n is the number of triangles used. If we take one of these triangles out of the picture you get something like this...

Posted by: Gelinde Cobbs

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