Brahmagupta (ब्रह्मगुप्त)

Indian astronomer and mathematician.

Born: c. 598 AD

Died: c. 670 AD

Discoveries

Astronomical Theory

Zero

In his magnum opus Brahmasphutasiddhanta, Brahmagupta was the first known mathematician to document on the arithmetic properties of zero as a number. The concept of zero as a number may have been known in India prior to Brahmagupta. Radiocarbon dating of the Bakhshali Manuscript (which included the symbol for zero) has revealed that parts of the document was written in the 4th century AD, the 7th century AD, and the 10th century AD.

Approximation of Pi

Brahmagupta used two approximations of pi:

$\pi = 3$

$\pi = \sqrt{10}$

Pell's Equation

Cyclic Quadrilaterals

Brahmagupta was famous for his studies on cyclic quadrilaterals. He discovered the formula for computing the area of a cyclic quadrilateral with sides $a,b,c,d$

$A = \sqrt{s(s-a)(s-b)(s-c)(s-d)}$

where $s = \frac{a+b+c+d}{2}$ is the semi-perimeter.