Character Catalog

Brahmagupta's masterwork in 25 chapters, it lays down the first arithmetic rules for zero and negative numbers, develops algebra, and presents advanced mathematical astronomy. Translated into Arabic in the 8th century, it directly influenced Al-Khwarizmi and Islamic mathematics.

A practical astronomical treatise in eight chapters, designed as an accessible companion to the Brahmasphutasiddhanta. It provides simplified tables for calculating planetary positions and eclipses, and was widely used by Indian and Arab astronomers.

A general rule for calculating the area of any cyclic quadrilateral (a four-sided figure inscribed in a circle) from the lengths of its four sides. This geometric discovery, presented in the Brahmasphutasiddhanta, goes beyond the work of Euclid and would not be rediscovered in Europe until the 17th century.

An algebraic formula showing that the product of two sums of two squares is itself a sum of two squares. Independently rediscovered by Fibonacci in the 13th century, it illustrates the remarkable lead that Indian mathematics held over the rest of the world at the time.

A geometry theorem about cyclic quadrilaterals stating that if the diagonals are perpendicular to each other, then the midpoint of one diagonal is the foot of the perpendicular drawn from that point to the other side. It stands as one of Brahmagupta's original contributions to plane geometry.

The sum of a positive and a negative number is their difference; if their absolute values are equal, the sum is zero. The sum of two negative numbers is negative, the sum of two positive numbers is positive.

This practical astronomical treatise, written in 665, provides simplified tables for calculating planetary positions and eclipses, intended for astronomers and astrologers at court.

Zero added to a positive or negative number is that number. Zero subtracted from a positive number is positive; subtracted from a negative number is negative. Zero multiplied by any number is zero.

It presents methods for solving quadratic equations and formulates theorems on arithmetic progressions, laying the groundwork for algebra as it would later be developed by Arab mathematicians.

Brahmagupta's birthplace, then the capital of the Gurjara kingdom. It was in this cultural and commercial hub of northwestern India that he received his early intellectual education.

A major intellectual and astronomical center of medieval India, where Brahmagupta directed the observatory and wrote his two landmark works. Ujjain also served as the reference meridian for Indian astronomers.

A great Buddhist monastic university — one of the largest in the medieval world — contemporary with Brahmagupta. It stands as a symbol of the intellectual vitality of 7th-century India, of which Brahmagupta was one of the foremost representatives.

Capital of the Abbasid Caliphate, where the Brahmasphutasiddhanta was translated into Arabic in the 8th century. This was the launching point for the spread of Indian mathematics — and the concept of zero — into Europe.