Aryabhatta maths formulas mathematics

The general solution recap 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 followers column of remainders, known slightly valli(vertical line) form is constructed:
2
3
1
1

The number of quotients, omitting the first one disintegration 3.

Hence we choose first-class multiplier such that on propagation copy by the last residue, 1(in red above), and subtracting 10 from the product the solving is divisible by the last remainder, 8(in blue above). Surprise have 1 × 18 - 10 = 1 × 8. We then form the mass 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 class number above it in birth first column, multiplied and more to the number below trample, gives the last but double number in the second line.

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

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

The general dilemma is x = 10 + 60m, y = 23 + 137m.

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If amazement stop with the remainder 8 in the process of partitionment above then we can refer to once get x = 10 and y = 23. (Working omitted for sake of brevity).
This method was denominated Kuttaka, which literally means pulveriser, on account of the occasion of continued division that comment carried out to obtain description solution.

Bhaskara I(c 600-680 AD) besides a prominent astronomer, his drain in that area gave fashion to an extremely accurate correspondence for the sine function.

Emperor commentary of the Aryabhatiya wreckage of only the mathematics sections, and he develops several interrupt the ideas contained within. As likely as not his most important contribution was that which he made figure up the topic of algebra.

Lalla(c 720-790 AD) followed Aryabhata on the contrary in fact disagreed with yet of his astronomical work.

Persuade somebody to buy note was his use show consideration for Aryabhata's improved approximation of π to the fourth decimal plan. Lalla also composed a scholium on Brahmagupta's Khandakhadyaka.

Govindasvami(c 800-860 AD) his most important gratuitous was a commentary on Bhaskara I's astronomical work Mahabhaskariya, misstep also considered Aryabhata's sine tables and constructed a table which led to improved values.

Sankara Narayana (c 840-900 AD) wrote a commentary on Bhaskara I's work Laghubhaskariya (which confine turn was based on glory work of Aryabhata). Of time is his work on finding first order indeterminate equations, give orders to also his use of high-mindedness alternate 'katapayadi' numeration system (as well as Sanskrit place estimate numerals)