Approximating Pi
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 $$3\frac{10}{71} < \pi < 3 \frac{1}{7}$$
What are the strengths and limitations of this method?
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