Chakravala Method: Algorithm, Indeterminate equation, Quadratic equation, Pell's equation, Bh?skara II, Brahmagupta, Sanskrit, Mathematical induction, ... Lagrange, Continued fraction, Square root - Softcover

Softcover

ISBN 10: 6130236204 ISBN 13: 9786130236205

Publisher: Alphascript Publishing, 2009

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The chakravala method is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly attributed to Bhāskara II, (c. 1114 – 1185 CE) although some attribute it to Jayadeva (c. 950 ~ 1000 CE). 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. E. 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 mathematical induction. The problems which were solved by Brahmagupta in 628 using the chakravala method were indeterminate quadratic equations, including Pell's equation for minimum integers x and y.

Edition details

• Publisher: Alphascript Publishing
• Publication date: 2009
• Language: English
• ISBN 10: 6130236204
• ISBN 13: 9786130236205
• Binding: Broché
• Number of pages: 120
• Editor: Miller Frederic P., Vandome Agnes F., McBrewster John