See Article History Brahmagupta, born —died c. He also had a profound and direct influence on Islamic and Byzantine astronomy. Brahmagupta was an orthodox Hindu, and his religious views, particularly the Hindu yuga system of measuring the ages of mankind, influenced his work. It was translated into Arabic in Baghdad about and had a major impact on Islamic mathematics and astronomy. In addition to expounding on traditional Indian astronomy in his books, Brahmagupta devoted several chapters of Brahma-sphuta-siddhanta to mathematics. He stressed the importance of these topics as a qualification for a mathematician, or calculator ganaka.

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He lived in Bhillamala modern Bhinmal during the reign of the Chavda dynasty ruler, Vyagrahamukha. He was the son of Jishnugupta and was a Shaivite by religion. However, he lived and worked there for a good part of his life. Prithudaka Svamin , a later commentator, called him Bhillamalacharya, the teacher from Bhillamala.

It was also a centre of learning for mathematics and astronomy. Brahmagupta became an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during this period. He studied the five traditional siddhanthas on Indian astronomy as well as the work of other astronomers including Aryabhata I , Latadeva, Pradyumna, Varahamihira , Simha, Srisena, Vijayanandin and Vishnuchandra.

Scholars state that he incorporated a great deal of originality to his revision, adding a considerable amount of new material. A good deal of it is astronomy, but it also contains key chapters on mathematics, including algebra, geometry, trigonometry and algorithmics, which are believed to contain new insights due to Brahmagupta himself.

He is presumed to have died in Ujjain. Controversy[ edit ] Brahmagupta directed a great deal of criticism towards the work of rival astronomers, and his Brahmasphutasiddhanta displays one of the earliest schisms among Indian mathematicians.

The division was primarily about the application of mathematics to the physical world, rather than about the mathematics itself. 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. The kingdom of Bhillamala seems to have been annihilated but Ujjain repulsed the attacks. The court of Caliph Al-Mansur — received an embassy from Sindh, including an astrologer called Kanaka, who brought possibly memorised astronomical texts, including those of Brahmagupta.

An immediate outcome was the spread of the decimal number system used in the texts. The mathematician Al-Khwarizmi — CE wrote a text called al-Jam wal-tafriq bi hisal-al-Hind Addition and Subtraction in Indian Arithmetic , which was translated into Latin in the 13th century as Algorithmi de numero indorum. Indian astronomic material circulated widely for centuries, even passing into medieval Latin texts. The rupas are [subtracted on the side] below that from which the square and the unknown are to be subtracted.

He further gave two equivalent solutions to the general quadratic equation Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminish that by half the unknown [and] divide [the remainder] by its square.

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## Indian mathematics

He wrote the Katyayana Sulba Sutra, which presented much geometry , including the general Pythagorean theorem and a computation of the square root of 2 correct to five decimal places. Jain mathematicians are important historically as crucial links between the mathematics of the Vedic period and that of the "classical period. In particular, their fascination with the enumeration of very large numbers and infinities led them to classify numbers into three classes: enumerable, innumerable and infinite. Not content with a simple notion of infinity, their texts define five different types of infinity: the infinite in one direction, the infinite in two directions, the infinite in area, the infinite everywhere, and the infinite perpetually. In addition, Jain mathematicians devised notations for simple powers and exponents of numbers like squares and cubes, which enabled them to define simple algebraic equations beejganita samikaran. Jain mathematicians were apparently also the first to use the word shunya literally void in Sanskrit to refer to zero. More than a millennium later, their appellation became the English word "zero" after a tortuous journey of translations and transliterations from India to Europe.

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## BRAHMAGUPTA: MATHEMATICIAN AND ASTRONOMER

He spent most of his life in Bhinmal which was under the rule of King Vyaghramukha. He was the head of the astronomical observatory at Ujjain which was the center of mathematics in India witnessing the work of many extraordinary mathematicians. Brahmagupta wrote many textbooks for mathematics and astronomy while he was in Ujjain. It contains a lot of criticism on the work of his rival mathematicians. Brahmagupta had many discrepancies with his fellow mathematicians and most of the chapters of this book talked about the loopholes in their theories. It had many rules of arithmetic which is part of the mathematical solutions now. Brahmagupta was the one to give the area of a triangle and the important rules of trigonometry such as values of the sin function.

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## Brahmagupta

The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral. Triangles Brahmagupta dedicated a substantial portion of his work to geometry. The base decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular [altitude] is the square-root from the square of a side diminished by the square of its segment. He further gives a theorem on rational triangles.

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Biography Brahmagupta — CE The great 7th Century Indian mathematician and astronomer Brahmagupta wrote some important works on both mathematics and astronomy. He was from the state of Rajasthan of northwest India he is often referred to as Bhillamalacarya, the teacher from Bhillamala , and later became the head of the astronomical observatory at Ujjain in central India. Most of his works are composed in elliptic verse, a common practice in Indian mathematics at the time, and consequently have something of a poetic ring to them. In his work on arithmetic, Brahmagupta explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots. He also gave rules for dealing with five types of combinations of fractions. Almost years later, in the 12th Century, another Indian mathematician, Bhaskara II, showed that the answer should be infinity, not zero on the grounds that 1 can be divided into an infinite number of pieces of size zero , an answer that was considered correct for centuries. Previously, the sum 3 — 4, for example, was considered to be either meaningless or, at best, just zero.