The polygon approximation method uses the perimeters of polygons to approximate pi and “was the first theoretical, rather than measured, calculation of pi,” but while it worked great for Archimedes in his time, it has limited practicality today (Groleau). In order to estimate pi, Archimedes used a circle that had a polygon inscribed in and circumscribed about it, then found the perimeter of each polygon, and used those values as the upper and lower limits of pi (Groleau). He started with a hexagon as the inner polygon of a circle with a diameter of 1 whose perimeter is equal to 6r when r is the radius of the circle (McKeeman). This meant that since the circumference of the circle was 2πr, 6r < 2πr an...
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...on (Bailey 55). The maximum number of digits employed in any practical way is a few thousands in order to answer mathematical questions using a computer (Bailey 55). One reason for the continued calculation pi is that, when calculated on computers, it can be used to test to hardware and software for errors, for example, when “some obscure hardware problems in one of the original Cray-2 supercomputers” were detected, but this could also be done with any other transcendental number (Bailey 55). The calculation of pi has also excited the advancement of computational techniques (Bailey 55). Even with these side effects, the main reason for the continuing calculation of pi lies the challenge, simply because “it is there” and curiosity is basic human nature (Bailey 55). We continue to strive to understand that magical number pi because we are curious where it will lead us.
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