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To estimate pi, Archimedes used the following steps: 1: First he started with a unit circle (circle with radius 1) 2: Then, he drew shapes with the same amount of sides both inside the circle and around the circle. For example he would draw a hexagon inside the circle so that the vertices were on the circle, as well as another hexagon outside the circle so that the sides touched the circle at one point. 3: since the area of the circle is pi, pi would have to be in between the areas on the outer (circumscribed) and inner (inscribed) polygons. Archimedes repeated these steps up to a 96-sided shape, calculating pi accurately to 2 decimal places.
