# Definition:Zu Chongzhi Fraction/Historical Note

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## Historical Note on Zu Chongzhi Fraction

The **Zu Chongzhi fraction** $\dfrac {355} {113}$ as an approximation for $\pi$ (pi) was derived by Zu Chongzhi and his son Zu Geng.

Adriaan Metius fortuitously rediscovered it independently around the $16$th century.

He did this by taking mediant of two limits $\dfrac {377} {120}$ and $\dfrac {333} {106}$ calculated by his father. This is guaranteed to generate a number between those limits, but the usefulness of the approximation was lucky.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41972 \ldots$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$