Brahmagupta

Brahmagupta (ब्रह्मगुप्त) (598-668) was an Indian mathematician and astronomer. He was the head of the astronomical observatory at Ujjain, and during his tenure there wrote two texts on mathematics and astronomy: the Brahma Sputa Siddhanta in 628, and the Khandakhadyaka in 665.

Mathematics

If there is a person to be assigned the most important discovery in all of mathemeatics, finding of zero, that would be Brahmagupta. The Brahmasphutasiddhanta, written circa 628 AD, 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 is not terribly useful; for instance, he states that 0/0 = 0.

Brahma Sputa Siddhanta has four and a half chapters devoted to pure math while the twelfth chapter, the Ganita, deals with arithmetic progressions and a bit of geometry. The eighteenth chapter of Brahmagupta's work is called the Kuttaka. This is usually associated with the Aryabhata's method for solving the indeterminate equation ax - by = c. But here Kuttaka means algebra. Brahmagupta was the inventor of the method of solving indeterminate equations of the second degree (equations of the form Nx² + 1 = y²). He was also the first to use algebra to solve astronomical problems. It was through Brahmagupta's Brahmasphutasiddhanta that the Arabs came to know of Indian astronomy. The Famous King Khalif Abbasid Al Mansoor (712-775) founded Baghdad, which is situated on the banks of the Tigris, and made it a center of learning. The King invited a scholar of Ujjain by the name of Kanka in 770 A.D. Kanka used the Brahmasphutasiddhanta to explain the Hindu system of arithmetic astronomy. Al Fazaii translated Brahmugupta's work into Arabic upon the request of the King.

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 attempted at constructing a square of area equalling that of a circle by assuming that pi would converge at sqrt(10). [1]

Astronomy

Some of the important contributions made by Brahmagupta in astronomy are: methods for calculations of the motions and places of various planets, their rising and setting, conjunctions, and the calculation of eclipses of the sun and the moon. Brahmagupta criticized the Puranic view that the earth was flat or hollow like a bowl. Instead, he observed that the earth and heaven were round. However he wrongly believed that the earth did not move.

See also

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

External links

• O'Connor, John J.; Robertson, Edmund F., "Brahmagupta", MacTutor History of Mathematics Archive, University of St Andrews