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Brahmagupta (ब्रह्मगुप्त) (Brahmagupta pronounced (help·info)) (598–668) was an Indian mathematician and astronomer. Brahmagupta was born in 598 A.D. in Bhinmal city in the states of Rajasthan of northwest India. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) in the empire of Harsha.

As a result Brahmagupta is often referred to as Bhillamalacarya, the teacher from Bhillamala Bhinmal. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote two texts on mathematics and astronomy: the Brahmasphutasiddhanta in 628, and the Khandakhadyaka in 665.

Contents 1 Mathematics 2 Astronomy 3 See also 4 External links

Brahmagupta popularized 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. It goes well beyond that, however, stating rules for arithmetic on negative numbers and zero which are quite close to the modern understanding. The major divergence is that Brahmagupta attempted to define division by zero, which is left undefined in modern mathematics. His definition of zero was quite accurate except he wrongly believed that 0/0 was equal to 0.

Brahmasphutasiddhanta has four and a half chapters devoted to pure mathematics while the twelfth chapter, the Ganita, deals with arithmetic progressions and some geometry. The eighteenth chapter of Brahmagupta's work is called the Kuttaka. This is usually associated with the Aryabhata's method for solving the Diophantine equation ax − by = c. But here Kuttaka means algebra. Brahmagupta went on to invent a method for solving Diophantine equations of the second degree, such as nx² + 1 = y².

Brahmagupta also gave the formula to find the area of any cyclic quadrilateral given its four sides. Heron's formula is a special case of this formula, when one of the sides equal zero. The relationship between the general Brahmagupta's formula and the Heron's formula is similar to how the law of cosines extends the Pythagorean theorem.

Brahmagupta gave a geometric construction for squaring the circle. It was not very accurate, since in modern terms it would amount to . [1]

Brahmagupta was the first to use algebra to solve astronomical problems. It was through the Brahmasphutasiddhanta that the Arabs learned of Indian astronomy. The famous Abbasid caliph Al-Mansur (712–775) founded Baghdad, which is situated on the banks of the Tigris, and made it a center of learning. The caliph invited a scholar of Ujjain by the name of Kankah in 770 A.D. Kankah used the Brahmasphutasiddhanta to explain the Hindu system of arithmetic astronomy. Al-Fazari translated Brahmugupta's work into Arabic upon the request of the caliph.

Some of the important contributions made by Brahmagupta in astronomy are: methods for calculating the position of heavenly bodies over time (ephemerides), their rising and setting, conjunctions, and the calculation of solar and lunar eclipses. Brahmagupta criticized the Puranic view that the Earth was flat or hollow like a bowl. Instead, he observed that the Earth and heaven were spherical. However he wrongly believed that the Earth did not move.

• Brahmagupta's formula
• Brahmagupta's identity
• Brahmagupta's theorem
• Brahmagupta interpolation formula
• Brahmagupta matrix
• Brahmagupta's problem
• Indian mathematics
• List of Indian mathematicians

• O'Connor, John J., and Edmund F. Robertson. "Brahmagupta". MacTutor History of Mathematics archive.
• Brahmagupta's theorem
• Brahmagupta's theorem II
• Brahmagupta's formula