# 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

**(BSS). BSS composed in A.D.628 contains 25 chapters. It deals with important astronomical and mathematical topics. The 12***Brahma-Sphuta-Siddhantha*^{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, ar^{2}, …….. are n terms of GP them**S=a(r**. Where a is the first terms and r the common ratio.^{n}-1)/r-1
Ü

**Quadratic Equation:**He also given a chapter on quadratic for solving the equation of the type ax^{2}+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 a

^{2}+b^{2}=c^{2}and d^{2}+e^{2}=f^{2}the quadrilateral (af,ce,bf,cd) is cyclic and its diagonals are at right angles. This figure is called brahmagupta’s trapezium.
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