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The chakravala method (Sanskrit: चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly attributed to Bhāskara II, (c. 1114 – 1185 CE)[1][2] although some attribute it to Jayadeva (c. 950 ~ 1000 CE).[3] Jayadeva pointed out that Brahmagupta's approach to solving equations of this type could be generalized, and he then described this general method, which was later refined by Bhāskara II in his Bijaganita treatise. He called it the Chakravala method: chakra meaning "wheel" in Sanskrit, a reference to the cyclic nature of the algorithm.[4] C.-O. Selenius held that no European performances at the time of Bhāskara, nor much later, exceeded its marvellous height of mathematical complexity.[1][4]
This method is also known as the cyclic method and contains traces of mathematical induction.[5]
- ^ a b Hoiberg & Ramchandani – Students' Britannica India: Bhaskaracharya II, page 200
- ^ Kumar, page 23
- ^ Plofker, page 474
- ^ a b Goonatilake, page 127 – 128
- ^ Cajori (1918), p. 197
"The process of reasoning called "Mathematical Induction" has had several independent origins. It has been traced back to the Swiss Jakob (James) Bernoulli, the Frenchman B. Pascal and P. Fermat, and the Italian F. Maurolycus. [...] By reading a little between the lines one can find traces of mathematical induction still earlier, in the writings of the Hindus and the Greeks, as, for instance, in the "cyclic method" of Bhaskara, and in Euclid's proof that the number of primes is infinite."