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A study on Sharaf al-Din al-Tusi’s numerical solution of cubic equations. (Chinese. English summary) Zbl 1349.01012

Summary: This article analyzes the numerical solutions of cubic equations based on comprehensive interpretations of Equations (1209) by Sharaf al-Din al-Tusi (1135–1213). The results show that the algorithms are constructed from existing methods of extracting roots. The article also compares the algorithms by al-Tusi and Qin Jiushao. Results indicate that the cores of the two algorithms are the same, though they are significantly different due to differences in the mathematical traditions. The present study is significant in understanding the numerical solutions of the cubic equations by al-Tusi. It also contributes to investigations of the features and traditions of such mathematical algorithms in China and Arabic countries.

MSC:

01A30 History of mathematics in the Golden Age of Islam
12-03 History of field theory
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
65-03 History of numerical analysis
65H05 Numerical computation of solutions to single equations

Biographic References:

al-Tusi, Sharaf al-Din
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