Dispelling mathematical doubts. Assessing the
mathematical correctness of algorithms in Bhâskara's commentary on the mathematical chapter of the Âryabhatîya.
Résumé
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.
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.
Cet article analyse le vocabulaire et les raisonnements que Bhâskara (629 A. D.) utilise pour justifier les procédures exposées dans le chapitre mathématique de l'Âryabhatîya, un traité d'astronomie en Sanskrit du cinquième siècle. Nous verrons qu'expliquer, montrer et vérifier des procédures font partie de l'effort général du commentaire pour défendre son interprétation des procédures et leur exactitude. Ces tentatives sont nullement systématiques, et quand elles apparaissent, elles sont souvent fragmentaires comme si elles étaient effectuées oralement. Nous discuterons néanmoins, de la méthode qui consiste à relire un algorithme à l'aide d'une autre. Nous verrons que la règle de trois et le théorème de Pythagore ont une valeur spéciale dans ce contexte.
Origine : Fichiers produits par l'(les) auteur(s)