Mathematics scientist brahmagupta biography

Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals. Where was brahmagupta born? Brahmagupta was born in the city of Bhinmal, Rajasthan. When was brahmagupta born? Brahmagupta was born in AD. When did brahmagupta die? Brahmagupta passed away in AD. Maths Program. Online Tutors. Math Tutors. Maths Games. Maths Puzzles.

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Mathematics scientist brahmagupta biography: Brahmagupta was the foremost Indian

Our Journey. Our Team. Commercial Maths. Maths Formulas. Multiplication Tables. United States. United Kingdom. Sri Lanka. His work had a profound influence on scholars in Byzantium, Islamic countries, and beyond. He introduced algebraic methods into astronomical computations and established rules for operations involving zero, positive, and negative quantities.

This monumental treatise consists of 25 chapters, largely devoted to astronomy, with two chapters 12th and 18th dedicated to pure mathematics. In this work, Brahmagupta advanced novel ideas and algorithms for various celestial phenomena, including eclipses, planetary positions, and timekeeping. The mathematical chapters of the Brahamasphutasiddhanta demonstrate Brahmagupta's expertise in arithmetic, algebra, and geometry.

XII Wiesbaden,83 - R C Gupta, Brahmagupta's formulas for the area and diagonals of a cyclic quadrilateral, Math. Education 8B 33 -B R C Gupta, Brahmagupta's rule for the volume of frustum-like solids, Math. Education 6B -B S Jha, A critical study on 'Brahmagupta and Mahaviracharya and their contributions in the field of mathematics', Math. Siwan 12 466 - T Kusuba, Brahmagupta's sutras on tri- and quadrilaterals, Historia Sci.

J Pottage, The mensuration of quadrilaterals and the generation of Pythagorean triads : a mathematical, heuristical and historical study with special reference to Brahmagupta's rules, Arch. History Exact Sci. Additional Resources show. Honours show. Honours awarded to Brahmagupta Popular biographies list Number 4. Cross-references show. Like the algebra of Diophantusthe algebra of Brahmagupta was syncopated.

Addition was indicated by placing the numbers side by side, subtraction by placing a dot over the subtrahend, and division by placing the divisor below the dividend, similar to our notation but without the bar. Multiplication, evolution, and unknown quantities were represented by abbreviations of appropriate terms. The four fundamental operations addition, subtraction, multiplication, and division were known to many cultures before Brahmagupta.

Brahmagupta describes multiplication in the following way:. The multiplicand is repeated like a mathematics scientist brahmagupta biography for cattle, as often as there are integrant portions in the multiplier and is repeatedly multiplied by them and the products are added together. It is multiplication. Or the multiplicand is repeated as many times as there are component parts in the multiplier.

Indian arithmetic was known in Medieval Europe as modus Indorum meaning "method of the Indians". The reader is expected to know the basic arithmetic operations as far as taking the square root, although he explains how to find the cube and cube-root of an integer and later gives rules facilitating the computation of squares and square roots.

Brahmagupta then goes on to give the sum of the squares and cubes of the first n integers. The sum of the squares is that [sum] multiplied by twice the [number of] step[s] increased by one [and] divided by three.

Mathematics scientist brahmagupta biography: Brahmagupta (c. – c. CE)

The sum of the cubes is the square of that [sum] Piles of these with identical balls [can also be computed]. Here Brahmagupta found the result in terms of the sum of the first n integers, rather than in terms of n as is the modern practice. He first describes addition and subtraction. The sum of a negative and zero is negative, [that] of a positive and zero positives, [and that] of two zeros zero.

A negative minus zero is negative, a positive [minus zero] is positive; zero [minus zero] is mathematics scientist brahmagupta biography. When a positive is to be subtracted from a negative or a negative from a positive, then it is to be added. The product of a negative and a positive is negative, of two negatives positive, and of positives positive; the product of zero and a negative, of zero and a positive, or of two zeros is zero.

But his description of division by zero differs from our modern understanding:. A positive divided by a positive or a negative divided by a negative is positive; a zero divided by zero is zero; a positive divided by a negative is negative; a negative divided by a positive is [also] negative. A negative or a positive divided by zero has that [zero] as its divisor, or zero divided by a negative or a positive [has that negative or positive as its divisor].

The square of a negative or positive is positive; [the square] of zero is zero. That of which [the square] is the square is [its] square root. The height of a mountain multiplied by a given multiplier is the distance to a city; it is not erased. When it is divided by the multiplier increased by two it is the leap of one of the two who make the same journey.

Also, if m and x are rational, so are dab and c. A Pythagorean triple can therefore be obtained from ab and c by multiplying each of them by the least common multiple of their denominators. The Euclidean algorithm was known to him as the "pulverizer" since it breaks numbers down into ever smaller pieces. The nature of squares: The product of the first [pair], multiplied by the multiplier, with the product of the last [pair], is the last computed.

The sum of the thunderbolt products is the first. The additive is equal to the product of the additives. The two square-roots, divided by the additive or the subtractive, are the additive rupas.

Mathematics scientist brahmagupta biography: Brahmagupta was a highly accomplished Indian

The key to his solution was the identity, [ 29 ]. Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure's area. 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. Although Brahmagupta does not explicitly state that these quadrilaterals are cyclic, it is apparent from his rules that this is the case. Brahmagupta dedicated a substantial portion of his work to geometry.

One theorem gives the lengths of the two segments a triangle's base is divided into by its altitude:. The base decreased and increased by the difference between the squares of the sides divided by the base; when divided by two they are the true segments. The perpendicular [altitude] is the square-root from the square of a side diminished by the square of its segment.

He further gives a theorem on rational triangles. A triangle with rational sides abc and rational area is of the form:. 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].

He continues to give formulas for the lengths and areas of geometric figures, such as the circumradius of an isosceles trapezoid and a scalene quadrilateral, and the lengths of diagonals in a scalene cyclic quadrilateral. This leads up to Brahmagupta's famous theorem. Imaging two triangles within [a cyclic quadrilateral] with unequal sides, the two diagonals are the two bases.

Their two segments are separately the upper and lower segments [formed] at the intersection of the diagonals.