Chakravala method

The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. Quotes about "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." Florian Cajori (1918), Origin of the Name "Mathematical Induction", The American Mathematical Monthly 25 (5), pp. 197–201. The method represents a best approximation algorithm of minimal length that, owing to several minimization properties, with minimal effort and avoiding large numbers automatically produces the best solutions to the equation. The chakravala method anticipated the European methods by more than a thousand years. But no European performances in the whole field of algebra at a time much later than Bhaskara's, nay nearly equal up to our times, equalled the marvellous complexity and ingenuity of chakravala. Clas-Olaf Selenius quoted in Goonatilake, Susantha (1998). Toward a Global Science: Mining Civilizational Knowledge. Indiana: Indiana University Press. ISBN 0-253-33388-1. This method is supreme above all praise; it is certainly the finest thing accomplished in number theory before Lagrange. Diese Methode ist über alles Lob erhaben; sie ist sicherlich das Feinste, was in der Zahlenlehre vor Lagrange geleistet wurde. On Bhaskara II's method Hankel, H.: Zur Geschichte der Mathematik im Altertum und Mittelalter, S. 202. Teubner, Leipzig (1874). External links Category:Mathematics