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.
Brahmagupta discovered the most important concept in all of mathematics, the zero. The
Brahmasphutasiddhanta, written circa 628 CE, 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 Nx
2 + 1 = y
2). 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]
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.
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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*
0 (number)
