## ब्रह्मगुप्त, शून्य व ऋणांक - अनुराग शर्मा

## Negative Numbers of Brahmagupta by Anurag Sharma

Indian mathematecian, poet, astrologer and astronomer Brahmagupta
(ब्रह्मगुप्त) was born in 598 CE (after famous mathematecians Aryabhatta and Bhaskara I) in Ujjain (Madhya Pradesh) or Bhinmal (Rajasthan). He is known for two works Brahmasphut Siddhanta (ब्रह्मस्फुटसिद्धान्त) and Khand Khadyak (खण्ड-खाद्यक)
describing zero and the negative numbers and elaborating mathematical operations
around these new entities.

The Indian mathematicians are known to have invented/discovered and used zero and negative numbers. First undisputed recorded evidence of use of negative numbers is available in "Brahma Sphuta Siddhanta", written by Indian mathematician Brahmagupta AKA Bhillamalacharya (भिल्लमाल आचार्य). Brahmagupta is known to have used negative numbers starting around 630 AD. During this time, positive numbers were used to represent assets and negative numbers were used to represent debt. He described the rules for the four basic operations on signed numbers-addition, subtraction, multiplication and division. He also pointed out that the square root of a positive number could be positive or negative. He is credited with a few other important mathematical contributions in areas of arithmetic, algebra and geometry. His treatment of quadratic equations and the quadratic formula, which can result in negative and irrational solutions, is of particular importance. Brahmagupta explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots.

Brahmagupta's other famous work is in geometry, his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure's area,

Abbasid caliph Al-Mansur (712–775) invited Kankah, a scholar of Ujjain in 770 A.D. Kankah used the Brahmasphutasiddhanta to explain the Hindu system of arithmetic astronomy. Muhammad al-Fazari translated Brahmugupta’s work "Brahmasphutasiddhanta" into Arabic on request of the caliph. Baghdad was the bridge between the mathematecians of India and Europe those days. Approximately one thousand years after Brahmagupta, Italian mathematician Girolamo Cardano described the negative numbers in a book titled The Great Art. The negative numbers were slowly accepted in circle of European mathematics later 16th century.

**© Anurag Sharma**