Chakravala method

The chakravala method is a cyclic <a href="/facts/Algorithm/fnl5NmRt">algorithm</a> to solve <a href="/facts/Indeterminate_equation/DwdC3hyK">indeterminate</a> <a href="/facts/Quadratic_equation/9IMnkJAT">quadratic equations</a>, including <a href="/facts/Pell%2527s_equation/n0ul61eQ">Pell's equation</a>. It is commonly attributed to <a href="/facts/Bh%25C4%2581skara_II/BQlUY9gA">Bhāskara II</a>, (c. 1114 – 1185 CE) although some attribute it to <a href="/facts/Jayadeva_(mathematician)/2IvWoJtY">Jayadeva</a> (c. 950 ~ 1000 CE). Jayadeva pointed out that <a href="/facts/Brahmagupta/f7uxKXo4">Brahmagupta</a>'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 <a href="/facts/Bijaganita/wr7jaubX">Bijaganita</a> treatise. He called it the Chakravala method: chakra meaning "wheel" in <a href="/facts/Sanskrit/ychfjhlx">Sanskrit</a>, a reference to the cyclic nature of the algorithm. C.-O. Selenius held that no European performances at the time of Bhāskara, nor much later, exceeded its marvellous height of mathematical complexity.
This method is also known as the cyclic method and contains traces of <a href="/facts/Mathematical_induction/KxAPqNrH">mathematical induction</a>.

Chakravala method open-in-new

Chakravala method