Archimedes' Limits to Value of Pi

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Theorem

The value of $\pi$ lies between $3 \frac {10} {71}$ and $3 \frac 1 7$:

$3 \dfrac {10} {71} < \pi < 3 \dfrac 1 7$


Proof


Historical Note

Archimedes demonstrated the limits to the value of $\pi$ in his Measurement of a Circle.


Sources