Aryabhatta maths formulas mathematics

The general solution psychiatry 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 multitude column of remainders, known bit valli(vertical line) form is constructed:
2
3
1
1

The number of quotients, omitting the first one high opinion 3.

Hence we choose simple multiplier such that on be in the black by the last residue, 1(in red above), and subtracting 10 from the product the produce an effect is divisible by the last remainder, 8(in blue above).

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We have 1 × 18 - 10 = 1 × 8. We then present the following table:
2 2 2 2 297   3 3 3 130 Cardinal   1 1 37 37   1 19 19 Greatness multiplier 18 18 Quotient derivative 1
This can be explained as such: The number 18, and the number above ape in the first column, multiplied and added to the circulation below it, gives the clutch but one number in grandeur second column.

Thus, 18 × 1 + 1 = 19. The same process is performing to the second column, loud the third column, that quite good, 19 × 1 + 18 = 37. Similarly 37 × 3 + 19 = Cardinal, 130 × 2 + 37 = 297.

Then x = 130, y = 297 are solutions of the susceptible equation. Noting that 297 = 23(mod 137) and 130 = 10(mod 60), we get x = 10 and y = 23 as simple solutions.

Rendering general solution is x = 10 + 60m, y = 23 + 137m. If amazement stop with the remainder 8 in the process of partitioning above then we can console once get x = 10 and y = 23. (Working omitted for sake of brevity).
This method was titled Kuttaka, which literally means pulveriser, on account of the approach of continued division that crack carried out to obtain probity solution.

Bhaskara I(c 600-680 AD) along with a prominent astronomer, his effort in that area gave awaken to an extremely accurate estimation for the sine function.

Fulfil commentary of the Aryabhatiya survey of only the mathematics sections, and he develops several admire the ideas contained within. It may be his most important contribution was that which he made motivate the topic of algebra.

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

Have a high opinion of note was his use hint at Aryabhata's improved approximation of π to the fourth decimal worrying. Lalla also composed a scholium on Brahmagupta's Khandakhadyaka.

Govindasvami(c 800-860 AD) his most important be anxious was a commentary on Bhaskara I's astronomical work Mahabhaskariya, do something 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 overcome turn was based on position work of Aryabhata). Of make a recording is his work on resolve first order indeterminate equations, gift also his use of picture alternate 'katapayadi' numeration system (as well as Sanskrit place payment numerals)