BRAHMGUPTA (598 AD – 668 AD)

Born	598 AD
*Died*	668 AD
*Residence*	Bhillamala (Gujarat boundary)
*Nationality*	Indian
*Fields*	Mathematics and astronomy

Brahmgupta is a renowned Indian astronomer and mathematician of 7^th century. He comes after Aryabhatt. Brahmgupta, son of Jisnu was born in A.D.598. His native place was Bhillamala. Bhillamala is an old name of the modern bhinmal, a village on the northern boundary of Gujarat.

Books:

v Brahmgupta, at the age of thirty, composed Brahma-Sphuta-Siddhantha (BSS). BSS composed in A.D.628 contains 25 chapters. It deals with important astronomical and mathematical topics. The 12^th and 18^th chapters are on arithmetic, geometry and algebra.

v He wrote the next book khandakhadyaka a treatise on astronomy in 587 saka. In khandakhadyaks, Brahmgupta suggest many improved methods.

His (Brahmagupta) Contributions

v Interest formula: He gave the formula for finding the simple interest as:

S.I = principle X rate X time / 100

v Zero rules :

Ü He explained the concept of zero. He defines zero as a-a=0

Ü According to him zero divided by zero is equal to zero

v Ratio rules: He also knew rules of ratio and proportion.

v Fractions:

Ü In writing fraction, he used the system of writing numerator and denominator.

Ü He explained the operations of addition, subtraction, multiplication and division with different types of fractions.

Ü In case of multiplication he wrote – “the product of the numerators divided by the product of the denominator is the multiplication of two or more fractions”

v Geometry:

Ü He gave the area of the triangle as s = route of s(s-a)(s-b)(s-c) where 2s = a+b+c and a,b,c are the sides of a triangle.

Ü He gave the formulae for finding the area of triangle in terms of base and height, ie Area = ½ base X height

Ü He also worked for finding the volume of plane figures.

Ü He gave 22/7 as the value of pie and suggested 3 as a practical value.

v Algebra Formula:

Ü In algebra, he made a considerable good work in the solution of equations involving more than one unknown quantity,

Ü He gave the rules for finding the sum of squares and cubes of natural numbers.

Ü Arithmetic progression: In arithmetic series he also gave formulae for the last term and sum of a given AP series.

I.e. L = s + a (n-1)d where a is the first term, d is the difference and n is the number of terms and s = n(n+1)/2 is the sum of n natural number if the fist term and difference is each equal to 1.

Ü Geometrical Progression: Similarly in GP series, the formula to find the sum of n terms was also given by him. Ie. a, ar, ar², …….. are n terms of GP them S=a(rⁿ-1)/r-1. Where a is the first terms and r the common ratio.

Ü Quadratic Equation: He also given a chapter on quadratic for solving the equation of the type ax²+px+q=0.

Ü Indeterminate Equation: He also gave solution for indeterminate equations.

Quadrilaterals:

Ü He made a fairly complete study of cyclic quadrilaterals.

Ü He also proved that if a²+b²=c² and d²+e²=f² the quadrilateral (af,ce,bf,cd) is cyclic and its diagonals are at right angles. This figure is called brahmagupta’s trapezium.

There is no doubt the Brahmagupta well understood the science of mathematics and astronomy. His work is quite elaborate and he contributed much of the development of mathematics and astronomy. His work gave guidance to several Indian astronomers.