Udayadivākara
Udayadivākara (c. 1073 CE) was an Indian astronomer and mathematician who has authored an influential and elaborate commentary, called Sundari, on Laghu-bhāskarīya of Bhāskara I. No personal details about Udayadivākara are known. Since the commentary Sundari takes the year 1073 CE as its epoch, probably the commentary was completed about that year. Sundari has not yet been published and is available only in manuscript form. Some of these manuscripts are preserved in the manuscript depositories in Thiruvananthapuram. According to K. V. Sarma, historian of the astronomy and mathematics of the Kerala school, Udayadivākara probably hailed from Kerala, India.[1][2]
Historical significance of Sundari
Apart from the fact that Sundari is an elaborate commentary, it has some historical significance. It has quoted extensively from a now lost work by a little known mathematician Jayadeva. The quotations relate to the cakravala method for solving indeterminate integral equations of the form . This shows that the method predates Bhaskara II contrary to generally held beliefs. Another important reference to Jayadeva’s work is the solution of the indeterminate equation of the form , being positive or negative.[2]
A problem and its solution
Udayadivākara used his method for solving the equation to obtain some particular solutions of a certain algebraic problem. The problem and Udayadivākara's solution to the problem are presented below only to illustrate the techniques used by Indian astronomers for solving algebraic equations.[2]
Problem
Find positive integers and satisfying the following conditions:
Solution
To solve the problem, Udayadivākara makes a series of apparently arbitrary assumptions all aimed at reducing the problem to one of solving an indeterminate equation of the form .
Udayadivākara begins by assuming that which can be written in the form . He next assumes that which, together with the earlier equation, yields
Now, Udayadivākara puts
which is then transformed to the equation
This equation is of the form with , and . Using the method for solving the equation , Udayadivākara finds the following solutions , and from which the values of and are obtained by back substitution.
See also
References
- ^ K. V. Sarma (1972). A History of the Kerala School of Hindu Astronomy. Vishveshvaranand Institute of Sanskrit and Indological Studies, Panjab University, Hoshiarpur. p. 45. Retrieved 28 January 2023.
- ^ a b c Aditya Kolachana, K. Mahesh and K. Ramasubramanian (2019). Studies in Indian Mathematics and Astronomy Selected Articles of Kripa Shankar Shukla. Hindustan Book Agency/Springer. pp. 133–152. (Chapter titled "Ācārya Jayadeva, the mathematician". Originally published in Ganita, Vol. 5, No. 1 (1954), pp. 1–20.)
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