# 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

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies