Brahmagupta (ब्रह्मगुप्त)

Indian astronomer and mathematician.

Born: c. 598 AD in Billamala

Died: c. 670 AD in Ujjain

Discoveries

Astronomical Theory

Brahmagupta opposed the ancient Vedic astronomers who argued that the Sun is closer to the Earth than the moon. He also compiled a sine table that is presented with astronomical data.

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 includes 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

Brahmagupta solved certain quadratic indeterminate equations of the form $Nx^2 + 1 = y^2$, which is called Pell's equation in the West. Pell's equation was intensively studied in ancient India after Brahmagupta, and his contributions paved the road to the general solution by Bhaskara II in the 12th century AD.

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.

He also discovered the property of orthodiagonal cyclic quadrilaterals, which is called the Brahmagupta theorem.