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Communication Dans Un Congrès Ganita Bharati (Indian Mathematics): Journal of the Indian Society for History of Mathematics Année : 2012

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

François Patte

Résumé

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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Dates et versions

hal-00584820 , version 1 (10-04-2011)

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  • HAL Id : hal-00584820 , version 1

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François Patte. The resolution of Diophantine equations according to Bhāskara and a justification of the cakravāla by Kṛṣṇadaivajña. Mathematics in Ancient Times, Aug 2010, Kozhikode, India. pp.73-105. ⟨hal-00584820⟩
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