Brahmagupta was born in Bhinmal, Indian, is Mathematician and Astronomer. Brahmagupta was a highly accomplished ancient Indian astronomer and mathematician who was the first to give rules to compute with zero. He is best remembered as the author of the theoretical treatise ‘Brāhmasphuṭasiddhānta’ ("Correctly established doctrine of Brahma"). He composed his texts in elliptic verse in Sanskrit, as was common practice in Indian mathematics of his time. The ‘Brāhmasphuṭasiddhānta’ was a seminal work in astronomy which went on have a deep influence not just in the development of astronomy in India, but also had a great impact on Islamic mathematics and astronomy. An orthodox Hindu, he took care not to antagonize his own religious leaders but was very bitter in criticizing the ideas advanced by rival astronomers hailing from the Jain religion. He was among the few thinkers of his era who had realized that the earth was not flat as many believed, but a sphere. He was much ahead of his contemporaries and his mathematical and astronomical calculations remained among the most accurate available for several centuries. He is believed to have written many works though only a few survive today. In addition to being an accomplished astronomer, he was also a much revered mathematician. His ‘Brāhmasphuṭasiddhānta’ is the first book that mentions zero as a number and also gives rules for using zero with negative and positive numbers.

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The difference between

rupas, when inverted and divided by the difference of the unknowns, is the unknown in the equation. Therupasare [subtracted on the side] below that from which the square and the unknown are to be subtracted.

1998

So Brahmagupta uses 3 as a "practical" value of π, and ${\sqrt {10}}\approx 3.1622\ldots$ as an "accurate" value of π. The error in this "accurate" value is less than 1%.

2010

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.

2013

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*.

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