Brahmagupta

Mathematician

1. BRAHMAGUPTABRAHMAGUPTA

2. 
Brahmagupta is one of the most Brahmagupta is one of the most
distinguished Mathematician and distinguished Mathematician and
Astronomer in the 7th century. He was the Astronomer in the 7th century. He was the
son of Vishnu Gupta and was born in son of Vishnu Gupta and was born in
Punjab. He lived in Ujjain and worked in Punjab. He lived in Ujjain and worked in
great astrological laboratory at Ujjain. He great astrological laboratory at Ujjain. He
wrote his first book ‘wrote his first book ‘Brahm-sp-huta-Brahm-sp-huta-
sidhantasidhanta’ or ‘’ or ‘BrahmasidhantaBrahmasidhanta’ at this ’ at this
place at the age of place at the age of 3030. It consists of . It consists of 2121
chapter and contains great knowledge on chapter and contains great knowledge on
arithmetic, geometry, algebra and arithmetic, geometry, algebra and
astronomy. astronomy.

3. 
He gave He gave 22/722/7 as value of as value of pp and suggested and suggested 33
as a practical value. In chapter an arithmetic, as a practical value. In chapter an arithmetic,
he has given a detailed account of progression, he has given a detailed account of progression,
areas of triangles and quadrilaterals, volumes areas of triangles and quadrilaterals, volumes
of trenches and slopes and amount of grains, in of trenches and slopes and amount of grains, in
heaps etc. He also invented four different heaps etc. He also invented four different
methods of multiplication, namelymethods of multiplication, namely
1.1. Gan MutrikaGan Mutrika
2.2. KhandaKhanda
3.3. BhedaBheda
4.4. IstaIsta

4. 
He explained the method of inversion for He explained the method of inversion for
the first time in the following way:the first time in the following way:
“ “Beginning from the end, make the Beginning from the end, make the
multiplier divisor, the divisor multiplier, multiplier divisor, the divisor multiplier,
make addition subtraction and subtraction make addition subtraction and subtraction
addition, make square, square-root and addition, make square, square-root and
square-root. This gives the required square-root. This gives the required
quantity.”quantity.”

5. 
He gave the method of squaring, cubing, He gave the method of squaring, cubing,
extracting square root as well as cube extracting square root as well as cube
root. Also he gave the exact concept of root. Also he gave the exact concept of
zerozero. He defined it as . He defined it as a-aa-a==0.0. He gave He gave
the following rules to deal with the following rules to deal with negative negative
numbersnumbers,,
1.1.Negative multiplied or divided by Negative multiplied or divided by
negative becomes positive.negative becomes positive.
2.2.Negative subtracted from zero is Negative subtracted from zero is
also positive.also positive.

6. 
He solved the equation He solved the equation xx
22
-10x-10x==-9-9 by a by a
rule which is equivalent to the quadratic rule which is equivalent to the quadratic
formula. formula. He multiplied the constant He multiplied the constant
term by the coefficient of xterm by the coefficient of x
22
, added , added
the square of half the coefficient of the square of half the coefficient of
x and found the square root of this x and found the square root of this
sum. He then subtracted half the sum. He then subtracted half the
coefficient of x and divided it by the coefficient of x and divided it by the
coefficient of xcoefficient of x
22
. The quotient gave . The quotient gave
the solution of the equation.the solution of the equation.

7. 
His works on arithmetic includes His works on arithmetic includes
integer, fractions, progressions, barter, integer, fractions, progressions, barter,
simple interest, the mensuration of plane simple interest, the mensuration of plane
figures and problems on volumes.figures and problems on volumes.

He found the formula for addition of He found the formula for addition of
geometrical progression,geometrical progression,
a+ar+ara+ar+ar
22
+…….n terms +…….n terms == a(r a(r
n - 1n - 1
)/r-1)/r-1

8. 
In the field of geometry, he elaborated In the field of geometry, he elaborated
upon the properties of right angled upon the properties of right angled
triangles and for the first time gave the triangles and for the first time gave the
solution of a right angled triangle by giving solution of a right angled triangle by giving
the following value of its sides;the following value of its sides;
aa==2mn; b2mn; b==mm
22
-n-n
22
; c; c==mm
22
+n+n
22
and and
a a==mm
1 / 21 / 2
;;
hh==(m/n-n)/2; c(m/n-n)/2; c==(m/n+n)/2 where (m/n+n)/2 where
m and n are two in equal integers.m and n are two in equal integers.

9. 
He also gave, for the first time, suggestions for the He also gave, for the first time, suggestions for the
construction of a cyclic quadrilateral having its sides as construction of a cyclic quadrilateral having its sides as
rational numbers. Two of the following formulae given by rational numbers. Two of the following formulae given by
him are in use even at present,him are in use even at present,
1.1.AreaArea of a cyclic quadrilateral having of a cyclic quadrilateral having a, b, ca, b, c and and d d as its as its
2.2.sidessides is equal to is equal to ÖÖ(s-a)(s-b)(s-c)(s-d)(s-a)(s-b)(s-c)(s-d) where where
a+b+c+da+b+c+d==2s, s 2s, s isis perimeter of the quadrilateral perimeter of the quadrilateral..
3.3.Length of one of the diagonalsLength of one of the diagonals of the cyclic of the cyclic
quadrilateral is equal to quadrilateral is equal to (bc+ad/ab+cd)(ac+bd)(bc+ad/ab+cd)(ac+bd)
4.4.Length of the other diagonalLength of the other diagonal is equal to is equal to
(ab+cd/bc+ad)(ac+bd)(ab+cd/bc+ad)(ac+bd)


Brahmagupta was the first Indian writer, who Brahmagupta was the first Indian writer, who
applied algebra to astronomy. He was a great applied algebra to astronomy. He was a great
mathematician, an astronomer and a poet. mathematician, an astronomer and a poet.

10. THANKYOUTHANKYOU