Casting Out Nines/Historical Note
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Historical Note on Casting Out Nines
The technique of Casting Out Nines was probably an invention of the mathematicians of early India.
It appears in Bhaskara II Acharya's Lilavati, dating from about $1150$.
It arrived in Western Europe from the Arabs, via the Liber Abaci of $1202$ by Leonardo Fibonacci.
When initially invented, the technique involved dividing the numbers involved by $9$ and adding the remainders, but the summing of the digital roots has the same effect.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $9$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $9$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): casting out nines
- 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $3$: Notations and Numbers: Brahmagupta, Mahavira and Bhaskara