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He calculated the perimeters of regular polygons inscribed within a unit circle and circumscribing the circle (outside the circle). The first is always less than the circumference of the circle ( = 2*pi) and the second is always more. As you increase the number of sides of the polygons, the polygons get closer and closer to the circle and their perimeters get nearer to the circumference.

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Q: How did Archimedes calculate pi?
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