By inscribing a circle in a square and then a square in a circle find an approximation to pi.
By using a hexagon, can you improve on the approximation? How much better an approximation is it?

Archimedes used this idea first with a hexagon, then a dodecagon (12 sides) and so on up to a 96 sided polygon to calculate pi and was able to establish that

${\displaystyle 3\frac{10}{71}<\pi <3\frac{1}{7}.}$

What are the strengths and limitations of this method?