Brahmagupta (c.AD 598–c.665)
Brahmagupta was a Hindu astronomer and mathematician who became the head of the observatory at Ujjain – the foremost mathematical center of India at this time; he was the last and most accomplished of the ancient Indian astronomers. His main work, Brahmasphutasiddhanta (The Opening of the Universe), written in 628, contains some remarkably advanced ideas, including a good understanding of the mathematical role of zero, rules for manipulating both positive and negative numbers, a method for computing square roots, methods of solving linear and some quadratic equations, and rules for summing series. His contributions to astronomy were equally ahead of their time. Brahmagupta's theorem states that in a cyclic quadrilateral (a four-sided shape whose corners lie on a circle) having perpendicular diagonals, the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.
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