Pi is defined as the ratio of the circumference of a circles to its diameter.
(pi as a symbol wasn't used until 1706)
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.
A Really Bad Example
The more sides the polygons have, the better the estimate of pi.
Archimedes used a polygon with 96 sides to show that the
value of pi was between
3 10/70 and 3 10/71 !
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