|Who is it?||Mathematician and Astronomer|
|Birth Place||Bhinmal, Indian|
|Died On||c. 668 CE|
|Known for||Zero Modern number system Brahmagupta's theorem Brahmagupta's identity Brahmagupta's problem Brahmagupta-Fibonacci identity Brahmagupta's interpolation formula Brahmagupta's formula|
The difference between rupas, when inverted and divided by the difference of the unknowns, is the unknown in the equation. The rupas are [subtracted on the side] below that from which the square and the unknown are to be subtracted.
So Brahmagupta uses 3 as a "practical" value of π, and as an "accurate" value of π. The error in this "accurate" value is less than 1%.
The Historian of science George Sarton called him "one of the greatest Scientists of his race and the greatest of his time." Brahmagupta's mathematical advances were carried on further by Bhāskara II, a lineal descendant in Ujjain, who described Brahmagupta as the ganaka-chakra-chudamani (the GEM of the circle of mathematicians). Prithudaka Svamin wrote commentaries on both of his works, rendering difficult verses into simpler language and adding illustrations. Lalla and Bhattotpala in the 8th and 9th centuries wrote commentaries on the Khanda-khadyaka. Further commentaries continued to be written into the 12th century.
In 665 Brahmagupta devised and used a special case of the Newton–Stirling interpolation formula of the second-order to interpolate new values of the sine function from other values already tabulated. The formula gives an estimate for the value of a function f at a value a + xh of its argument (with h > 0 and −1 ≤ x ≤ 1) when its value is already known at a − h, a and a + h.