BRAHMAGUPTA

Brahmagupta was an Indian mathematician and astronomer

who wrote two important works on mathematics: the

Brahmasphutasiddhanta and the Khandakhadyaka and he was the first mathematician to use the concept of the zero. But right now people don't know

where Brahmagupta's mathematics are derivated from.

1.Mathematics.

1.1.Arithmetic.

Four fundamental operations (addition,subtraction,multiplication and

division)were know to many cultures before Brahmagupta. This current system is based on

the Hindu Arabic number system. Indian arithmetic was know in Medieval Europe as

“Modus Indoram”.

-Series and zero.

*Series: He gives the sum of the squares of the first natural numbers and the sum of the cubes of

the first natural numbers.

*Zero: The Brahmasphutasiddhanta was the first book that mentions zero as a number, so

Brahmagupta is considered the first to formulate the concept of this number.

1.2. Algebra.

Brahmagupta gave the solucion of the general linear equation. He solved systems of

simultaneous indeterminate equations leaving alone the desired variable and then dividing it by

the coefficient.

1.3. Geometry.

-Brahmagupta's formula.

Bramagupta's most famous result in geometry is his formula for cyclic quadrilaterals. Giving him

the lenghts of the sides of any cyclic quadrilateral, Brahmagupta gave an exact formula for the

figure's area.

-Triangles.

Brahmagupta dedicated a big portion of his work to geometry. The base decreased and increased

by the difference between the squares of the sides divided by the base.

-Brahmagupta's theorem.

The square-root of the sum of the two products of the sides of a non-unequal quadrilateral is the

diagonal.

1.4 Trigonometry

In 665 Brahmagupta devised and used a special case of the Newton-Stirling interpolation formula of the second order to interpolate new values of

the sine function from other values already tabulated.

-Interpolation formula.