Bakhshali square-root method
Método de Bakhshali para raíces cuadradas
- Date
- c. siglos VIII-XI · confidence low
- Place
- Bakhshali, Mardan, Khyber Pakhtunkhwa, Pakistan
- Credited to
- Unknown author (Bakhshali manuscript)
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Algorithm that corrects an initial approximation of a square root with a second-order term, equivalent to two steps of the Newton-Raphson method. For √41 it gives 6.403139 against the true value of 6.403124: four correct decimal places.
The 2017 radiocarbon dating (Bodleian) gave very different dates for different folios (3rd, 8th and 10th centuries), which remain much disputed.
What it led to
- high-precision arithmetic calculation
- Indian tradition of iterative algorithms