Archimedes Traps Pi

Pi is defined as the ratio of the circumference of a circles to its diameter.

(pi as a symbol wasn't used until 1706)

How did Archimedes estimate the value of pi?

He drew two polygons around the circle's center -
one outside the circle (circumscribed) so its perimeter was greater than the circle's,  and
one inside the circle (inscribed) so its perimeter was less than the circle's.

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