# Why is Brahmagupta considered a great mathematician

bettermarks »Math glossary» Brahmagupta

**Surname: **Brahmagupta

**Born: **around 598 in the northwest of what is now India

**Died: **around 670 probably in Ujjain (India)

**Teaching / research areas**: Number theory, algebra, geometry, astronomy

Brahmagupta was a 7th century Indian astronomer and mathematician. His main work *Brahmasphutasiddhanta* had a great influence on the Arab scholars and his findings later found their way into medieval Europe through translations from Arabic. Brahmagupta can be called the discoverer of the number zero. He also expanded mathematics to include arithmetic, algebra and geometry, three of which bear his name: the *Brahmagupta identity*, the *Brahmagupta's theorem* and the *Formula of Brahmagupta*.

**Life**

Brahmagupta was born around 600 in the northwest of what is now India. He headed the astronomical observatory in Ujjain and in this capacity wrote several papers on mathematics and astronomy, of which *Brahmasphutasiddhanta* (in German about "beginning of the universe") is the most famous. As was customary in India back then, it is written in verse.

**The discovery of the number zero**

The Brahmasphutasiddhanta is the first known text in which the zero is treated as a separate number (previously the zero was only used as a placeholder). In contrast to modern mathematics, in which quotients with the divisor 0 are not defined, Brahmagupta also allowed division by 0. He established rules for calculating with zero, positive and negative numbers, which are largely our modern understanding correspond.

**The Brahmagupta Identity**

In Brahmasphutasiddhanta, Brahmagupta also provides the one named after him *Brahmagupta identity* (also *Brahmagupta – Fibonacci identity*), which describes how the product of two sums, each consisting of two square numbers, can again be represented as the sum of two other square numbers. It is:

\ ((a ^ 2 + b ^ 2) (c ^ 2 + d ^ 2) = (ac + bd) ^ 2 + (ad-bc) ^ 2 = (ac-bd) ^ 2 + (ad + bc) ^ 2 \)

From the identity it follows directly that the product of two sums of squares is again a sum of squares.

**On the geometry of quadrilateral tendons: Brahmagupta's theorem and formula**

Two other famous results of Brahmagupta concern the geometry of quadrilateral tendons. The *Brahmagupta's theorem* describes a side bisection in certain quadrilateral tendons and with the *Formula of Brahmagupta* calculate the area of an arbitrary chordal quadrilateral.

As an astronomer, Brahmagupta made calculations on the position of celestial bodies and on the explanation of solar and lunar eclipses.

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