The resolution of Diophantine equations according to Bhāskara and a justification of the cakravāla by Kṛṣṇadaivajña

Abstract : The main goal of this paper is to present an Indian 'demonstration' of the cakravāla rules provided by Bhāskara II. This demonstration was given by Kṛṣṇadaivajña, a mathematician who lived at the end of the sixteenth century, in his commentary on Bhāskara's Bījagaṇita: the Bījapallava. The cakravāla, or cyclic method, is a procedure to calculate the solutions of a Diophantine quadratic equation of the form: $p\,x^2 + k = y^2$. This cyclic method involves solving linear Diophantine equations, so we will make a presentation, as short as possible, of the rules given by Bhāskara in order to handle these linear and quadratic equations: the kuṭṭaka and the vargaprakṛti. When necessary, we will present commentators' explanations.
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S.G. Dani. Mathematics in Ancient Times, Aug 2010, Kozhikode, India. MD Publications Pvt Ltd New Delhi, 32 (1-2), pp.73-105, 2012

https://hal.archives-ouvertes.fr/hal-00584820
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Dernière modification le : mardi 11 octobre 2016 - 14:22:15
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François Patte. The resolution of Diophantine equations according to Bhāskara and a justification of the cakravāla by Kṛṣṇadaivajña. S.G. Dani. Mathematics in Ancient Times, Aug 2010, Kozhikode, India. MD Publications Pvt Ltd New Delhi, 32 (1-2), pp.73-105, 2012. <hal-00584820>

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