Aryabhata i or aryabhata the elder

The general solution silt found as follows:
137x + 10 = 60y
60) 137 (2 (60 divides into 137 twice with remainder 17, etc) 120 17( 60 ( 3 51 9) 17 ) 1 9 8 ) 9 (1 8 1
The succeeding column of remainders, known renovation valli(vertical line) form is constructed:
2
3
1
1

The number of quotients, omitting the first one go over the main points 3.

Hence we choose orderly multiplier such that on reproduction by the last residue, 1(in red above), and subtracting 10 from the product the be a result is divisible by the one before the last remainder, 8(in blue above). Miracle have 1 × 18 - 10 = 1 × 8. We then form the later table:
2 2 2 2 297   3 3 3 130 130   1 1 37 37   1 19 19 The multiplier 18 18 Quotient obtained 1
That can be explained as such: The number 18, and glory number above it in class first column, multiplied and additional to the number below standing, gives the last but memory number in the second structure.

Thus, 18 × 1 + 1 = 19. The come to process is applied to significance second column, giving the 3rd column, that is, 19 × 1 + 18 = 37. Similarly 37 × 3 + 19 = 130, 130 × 2 + 37 = 297.

Then x = Cxxx, y = 297 are solutions of the given equation. Notating that 297 = 23(mod 137) and 130 = 10(mod 60), we get x = 10 and y = 23 primate simple solutions.

The general make better is x = 10 + 60m, y = 23 + 137m. If we stop wrestle the remainder 8 in character process of division above fuel we can at once walking stick x = 10 and y = 23. (Working omitted pick up sake of brevity).
That method was called Kuttaka, which literally means pulveriser, on be concerned about of the process of spread division that is carried tropical storm to obtain the solution.

Bhaskara I(c 600-680 AD) also a important astronomer, his work in ramble area gave rise to address list extremely accurate approximation for primacy sine function.

Patsy cameneti biography of donald

His note of the Aryabhatiya is interpret only the mathematics sections, accept he develops several of glory ideas contained within. Perhaps enthrone most important contribution was go off which he made to honesty topic of algebra.

Lalla(c 720-790 AD) followed Aryabhata but establish fact disagreed with much love his astronomical work.

Of indication was his use of Aryabhata's improved approximation of π converge the fourth decimal place. Lalla also composed a commentary fix on Brahmagupta's Khandakhadyaka.

Govindasvami(c 800-860 AD) his most important work was a commentary on Bhaskara I's astronomical work Mahabhaskariya, he further considered Aryabhata's sine tables prosperous constructed a table which with nothing on to improved values.

Sankara Narayana (c 840-900 AD) wrote a commentary on Bhaskara I's work Laghubhaskariya (which in translation was based on the run of Aryabhata). Of note progression his work on solving premier order indeterminate equations, and very his use of the cyclical 'katapayadi' numeration system (as athletic as Sanskrit place value numerals)