RGUKT

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Born : 598 AD, Bhinmal in Rajhasthan

Died : 670 AD, India

Works : * Brahmagupta was the first to give rules to compute with zero

* Brahmagupta gave the solution of the general linear equation as bx + c = dx + e equivalent to x = e − c/b − d

* Brahmagupta then goes on to give the sum of the squares and cubes of the first n integers sum of the squares of the first n natural numbers as n(n + 1)(2n + 1)/6 sum of the cubes of the first n natural numbers as (n(n + 1)/2)^2 * Brahmagupta states that 0/0 is undefined * He described about addition, subtraction, multiplication and division of two positive or negative numbers. * The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate [area] is the square root from the product of the halves of the sums of the sides diminished by [each] side of the quadrilateral.

So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area is

(p + r)/2 · (q + s)/2 while, letting t = (p + q + r + s)/2, the exact area is

√(t − p)(t − q)(t − r)(t − s). * Lengths of the two segments a triangle's base is divided into by its altitude: 1/2[b ± (c^2 − a^2/b)]. * The interpolation formula (which can be used to find the missing value. However, by drawing a straight line through two points on a curve, the value at other points on the curve can be approximated. In the formula for interpolation, x-sub1 and y-sub1 represent the first set of data points of the values observed).

* He gave a Diophantus identity ( express the product of two sums of two squares as a sum of two squares in two different methods) (a^2+b^2)(c^2+d^2) = (ac-bd)^2+(ad+bc)^2 =(ac+bd)^2+(ad-bc)^2

His famous book is “Brahma-sphutha-sidhanta” ``