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 the 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): $3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Zu Chongzhi (Tsu Chung Chi) (ad 429-500)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Zu Chongzhi (Tsu Chung Chi) (ad 429-500)