ब्रह्मगुप्त
Brahmagupta (598–668 AD) was a great Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. He was from the state of Rajasthan of northwest India (he is often referred to as Bhillamalacarya, the teacher from Bhillamala), and later became the head of the astronomical observatory at Ujjain in central India. His best known work is the Brahmasphutasiddhanta (Correctly Established Doctrine of Brahma), written in 628 in Bhinmal. In deals with Algebra, Trigonometry and geometry. Brahmagupta started the study about ‘zero’, he made many experiments with zero and researched about dividing any number with zero. Today we call the answer as infinity. However, on that time he called it as “Khachedam”.
Contribution of Brahmagupta to mathematics
- Algebra : Brahmagupta gave the solution of the general linear equation and also gave two equivalent solutions to the general quadratic equation ax2 + bx + c = 0.
- Arithmetic : Four fundamental operations (addition, subtraction, multiplication and division) were known to many cultures during the period of Brahmagupta.
- Brahmagupta details operations on fractions, square root and also explains how to find the cube and cube-root of an integer and later gives rules facilitating the computation of squares and square roots.
- Series : Brahmagupta then goes on to give the sum of the squares and cubes of the first n integers.
- Zero : In his book mentions that, zero as a number and is also considered as the first to formulate the concept of zero. He gave rules of using zero with negative and positive numbers.
- Multiplication : He gave rules for the product of signed integers.
- Geometry : Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals. 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.
- Brahmagupta's theorem : The square-root of the sum of the two products of the sides and opposite sides of a non-unequal quadrilateral is the diagonal. The square of the diagonal is diminished by the square of half the sum of the base and the top; the square-root is the perpendicular [altitudes].
- Trigonometry : In chapter 2 of his Brahmasphutasiddhanta, entitled Planetary True Longitudes, Brahmagupta presents a sine table using names of objects to represent the digits of place-value numerals, as was common with numerical data in Sanskrit treatises, which again can be translated into the list of sines, 214, 427, 638, 846, 1051, 1251, 1446, 1635, 1817, 1991, 2156, 2312, 1459, 2594, 2719, 2832, 2933, 3021, 3096, 3159, 3207, 3242, 3263, and 3270, with the radius being 3270.