29 Facts About Brahmagupta

Brahmagupta is the author of two early works on mathematics and astronomy: the Brahmasphutasiddhanta, a theoretical treatise, and the Khandakhadyaka, a more practical text.

Brahmagupta was the first to give rules for computing with zero.

The texts composed by Brahmagupta were in elliptic verse in Sanskrit, as was common practice in Indian mathematics.

In 628 CE, Brahmagupta first described gravity as an attractive force, and used the term "gurutvakarsanam " in Sanskrit to describe it.

Brahmagupta was born in 598 CE according to his own statement.

Brahmagupta lived in Bhillamala in Gurjaradesa during the reign of the Chavda dynasty ruler, Vyagrahamukha.

Brahmagupta was the son of Jishnugupta and was a Hindu by religion, in particular, a Shaivite.

Brahmagupta lived and worked there for a good part of his life.

Brahmagupta became an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during this period.

Brahmagupta studied the five traditional Siddhantas on Indian astronomy as well as the work of other astronomers including Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin and Vishnuchandra.

Later, Brahmagupta moved to Ujjaini, Avanti, a major centre for astronomy in central India.

Brahmagupta died in 668 CE, and he is presumed to have died in Ujjain.

Brahmagupta's texts were translated into Arabic by Muhammad al-Fazari, an astronomer in Al-Mansur's court, under the names Sindhind and Arakhand.

Brahmagupta gave the solution of the general linear equation in chapter eighteen of Brahmasphutasiddhanta,.

Brahmagupta further gave two equivalent solutions to the general quadratic equation.

Brahmagupta went on to solve systems of simultaneous indeterminate equations stating that the desired variable must first be isolated, and then the equation must be divided by the desired variable's coefficient.

Brahmagupta then goes on to give the sum of the squares and cubes of the first integers.

Brahmagupta gives the sum of the squares of the first natural numbers as and the sum of the cubes of the first n natural numbers as.

Brahmagupta's Brahmasphutasiddhanta is the first book that provides rules for arithmetic manipulations that apply to zero and to negative numbers.

In chapter eighteen of his Brahmasphutasiddhanta, Brahmagupta describes operations on negative numbers.

In chapter twelve of his Brahmasphutasiddhanta, Brahmagupta provides a formula useful for generating Pythagorean triples:.

Brahmagupta went on to give a recurrence relation for generating solutions to certain instances of Diophantine equations of the second degree such as by using the Euclidean algorithm.

Brahmagupta dedicated a substantial portion of his work to geometry.

In some of the verses before verse 40, Brahmagupta gives constructions of various figures with arbitrary sides.

Brahmagupta finds the volume of rectangular prisms, pyramids, and the frustum of a square pyramid.

Brahmagupta further finds the average depth of a series of pits.

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.

In chapter seven of his Brahmasphutasiddhanta, entitled Lunar Crescent, Brahmagupta rebuts the idea that the Moon is farther from the Earth than the Sun.

Brahmagupta explains that since the Moon is closer to the Earth than the Sun, the degree of the illuminated part of the Moon depends on the relative positions of the Sun and the Moon, and this can be computed from the size of the angle between the two bodies.