Brahmagupta

Brahmagupta (589–668) was an Indian mathematician and astronomer.Brahmagupta was born in 598 CE in Bhinmal city in the state of Rajasthan of northwest India. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) in the empire of Harsha during the reign (and possibly under the patronage) of King Vyaghramukha. As a result, Brahmagupta is often referred to as Bhillamalacarya, that is, the teacher from Bhillamala Bhinmal. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote four texts on mathematics and astronomy: the Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672.

Brahmagupta's most famous work is his Brahmasphutasiddhanta. It is composed in elliptic verse, as was common practice in Indian mathematics, and consequently has a poetic ring to it. As no proofs are given, it is not known how Brahmagupta's mathematics was derived.

Famous extracts from Brahmasphutasiddhanta
Algebra
The solution of the general linear equation
Arithmetic Series
The sum of the squares and cubes of the first n integers.He gives the sum of the squares of the first n natural numbers as n(n+1)(2n+1)/6 and the sum of the cubes of the first n natural numbers as (n(n+1)/2)².
Zero
Brahmagupta made use of an important concept in mathematics, the number zero. The Brahmasphutasiddhanta is the earliest known text to treat zero as a number in its own right. He first describes addition and subtraction, multiplication and division.
Diophantine analysis
Pythagorean triples
Pell's equation
Nx2 + 1 = y2 (called Pell's equation) by using the Euclidean algorithm. The Euclidean algorithm was known to him as the "pulverizer" since it breaks numbers down into ever smaller pieces.
Geometry
Brahmagupta's formula
Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals.
Pi
He gives values of [pi]
Measurements and constructions
Trigonometry
Sines
Astronomy

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