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although in modern colors - a

square circumscribed around a

circle. Archimedes concluded

that the actual perimeter of the

circle must be less than the

perimeter of the circumscribed

square and greater than the

perimeter of the inscribed

square. It was an easy leap (for

him) to realize that the actual

perimeter of the circle could be

approached by increasing the

number of sides of the

circumscribed polygons.