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
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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