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Dispelling mathematical doubts. Assessing the mathematical correctness of algorithms in Bhâskara’s commentary on the mathematical chapter of the Âryabhatîya

Dispelling mathematical doubts. Assessing the mathematical correctness of algorithms in Bhâskara’s commentary on the mathematical chapter of the Âryabhatîya

By Agathe Keller

Published Online (2008)

Abstract:  In the mathematical chapter of the Âryabhatîya, a Sanskrit astronomical treatise of the fifth century, Bhâskara (629 ad) established procedures for checking the computational accuracy and logical consistency of mathematical exercizes. Through the explanations, demonstrations and verifications of his commentary, Bhâskara endeavored to defend his interpretation of the procedures and their correctness. These unsystematic attempts at justification are often fragmentary and perhaps mere echoes of an activity carried out orally. Nonetheless, one of the modes for mathematically grounding a procedure was `re-interpretation’ via the Rule of Three and the `Pythagorean Theorem’. Another mode of assessing the validity of a procedure was to establish an independant alternative procedure arriving at the same result.

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