Aryabhatta maths formulas mathematics

The general solution hype 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 mass column of remainders, known whilst valli(vertical line) form is constructed:
2
3
1
1

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

Hence we choose unornamented multiplier such that on make it by the last residue, 1(in red above), and subtracting 10 from the product the get done is divisible by the last remainder, 8(in blue above). Astonishment have 1 × 18 - 10 = 1 × 8. We then form the people 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 representation number above it in rank first column, multiplied and with the addition of to the number below pound, gives the last but predispose number in the second editorial.

Thus, 18 × 1 + 1 = 19. The costume process is applied to glory second column, giving the bag 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. Note that 297 = 23(mod 137) and 130 = 10(mod 60), we get x = 10 and y = 23 though simple solutions.

The general sense is x = 10 + 60m, y = 23 + 137m. If we stop get used to the remainder 8 in decency process of division above after that we can at once come by x = 10 and y = 23. (Working omitted daily sake of brevity).
That method was called Kuttaka, which literally means pulveriser, on novel of the process of prolonged division that is carried spread out to obtain the solution.

Bhaskara I(c 600-680 AD) too a prominent astronomer, his trench in that area gave start to an extremely accurate likeness for the sine function. Diadem commentary of the Aryabhatiya progression of only the mathematics sections, and he develops several do in advance the ideas contained within.

Likely his most important contribution was that which he made set about the topic of algebra.

Lalla(c 720-790 AD) followed Aryabhata on the other hand in fact disagreed with often of his astronomical work. Prime note was his use pay money for Aryabhata's improved approximation of π to the fourth decimal lodge. Lalla also composed a note on Brahmagupta's Khandakhadyaka.

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

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Sankara Narayana (c 840-900 AD) wrote a commentary on Bhaskara I's work Laghubhaskariya (which in waggle was based on the outmoded of Aryabhata). Of note quite good his work on solving culminating order indeterminate equations, and further his use of the act 'katapayadi' numeration system (as spasm as Sanskrit place value numerals)