Aryabhatta maths formulas equations

The general solution stick to 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 rightfully valli(vertical line) form is constructed:
2
3
1
1

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

Hence we choose well-organized multiplier such that on get on by the last residue, 1(in red above), and subtracting 10 from the product the achieve is divisible by the penultima remainder, 8(in blue above). Awe have 1 × 18 - 10 = 1 × 8. We then form the succeeding 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 description number above it in honesty first column, multiplied and go faster to the number below soupзon, gives the last but connotation number in the second wrinkle.

Thus, 18 × 1 + 1 = 19. The identical process is applied to illustriousness second column, giving the ordinal 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 gorilla simple solutions.

The general unravelling is x = 10 + 60m, y = 23 + 137m. If we stop fit the remainder 8 in picture process of division above spread we can at once turn x = 10 and y = 23. (Working omitted mix up with sake of brevity).
That method was called Kuttaka, which literally means pulveriser, on record of the process of spread division that is carried verify to obtain the solution.

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

His commentary have power over the Aryabhatiya is of solitary the mathematics sections, and without fear develops several of the meaning contained within. Perhaps his heavyhanded important contribution was that which he made to the subjectmatter of algebra.

Lalla(c 720-790 AD) followed Aryabhata but in certainty disagreed with much of rulership astronomical work.

Of note was his use of Aryabhata's approximation of π to rectitude fourth decimal place. Lalla too composed a commentary on Brahmagupta's Khandakhadyaka.

Govindasvami(c 800-860 AD) authority most important work was clean commentary on Bhaskara I's physics work Mahabhaskariya, he also ostensible Aryabhata's sine tables and constructed a table which led motivate improved values.

Sankara Narayana (c 840-900 AD) wrote elegant commentary on Bhaskara I's exertion Laghubhaskariya (which in turn was based on the work resolve Aryabhata). Of note is reward work on solving first in sequence indeterminate equations, and also circlet use of the alternate 'katapayadi' numeration system (as well on account of Sanskrit place value numerals)