The Chakravala method is a cyclic algorithm to solve quadratic integer equations. Its roots go to early Indian mathematics summarized by Aryabhata which was later developed further by Brahmagupta, Jayadeva (mathematician), and Bhaskara II. Aryabhata (आरà¥à¤¯à¤à¤Ÿ) Ä€ryabhaá¹a) (476 - 550) is the first of the great astronomers of the classical age of India. ... Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ... Jayadeva (जयदेव), 9th century Indian mathematician, knew the cyclic method (cakravala) that was called by Hermann Hankel as the finest thing achieved in the theory of numbers before Lagrange (18th century). ... BhÄskara (1114-1185), also called BhÄskara II and BhÄskarÄcÄrya (Bhaskara the teacher) was an Indian mathematician. ...
The Brahmagupta problem related to the Chakravala method is the solution to problems such as 61x^2 + 1 = y^2 for minimum integers x and y. Jayadeva and Bhaskara II offered the first complete solution Brahmagupta (ब्रह्मगुप्त) (598_668) was an Indian mathematician and astronomer. ... Jayadeva Goswami was a composer of Hindu hymns and poetic works, including especially the Sanskrit work, the Gita Govinda, a now-famous work on the divine love of the Hindu god Krishna. ... BhÄskara (1114-1185), also called BhÄskara II and BhÄskarÄcÄrya (Bhaskara the teacher) was an Indian mathematician. ...
x = 226 153 980 and y = 1 766 319 049.
This was solved first in Europe by Lagrange, but his method requires the calculation of twenty-one successive convergents of the continued fraction for the square root of 61 while the Chakravala method is much simpler. Joseph Louis Lagrange Joseph Louis Lagrange (January 25, 1736 – April 10, 1813; born Giuseppe Luigi Lagrangia in Turin, Lagrange moved to Paris (1787) and became a French citizen, adopting the French translation of his name, Joseph Louis Lagrange) was an Italian mathematician and astronomer who made important contributions to classical...
References
C-O Selenius, Rationale of the chakravala process of Jayadeva and Bhaskara II, Historia Math. 2 (1975), 167-184.
C-O Selenius, Kettenbruch theoretische Erklarung der zyklischen Methode zur Losung der Bhaskara-Pell-Gleichung, Acta Acad. Abo. Math. Phys. 23 (10) (1963).
Feeds |
Contact