Question

i am looking for a project on the contribution of mathmatician

Answer 1

refer to the above attachment

Answer 2

heya mate..!!

OK fine if this is your topic then you can search for mathematicians like aryabhatta, Ramanujan, etc.. if it is based on India and you can search for their childhood and their discoveries..

hope it helps you.. plz mark as brainliest..

BRAHMAGUPTA :-

Brahmagupta gave the solution of the general linear equation in chapter eighteen of Brahmasphutasiddhanta,

The difference between rupas, when inverted and divided by the difference of the unknowns, is the unknown in the equation. The rupas are [subtracted on the side] below that from which the square and the unknown are to be subtracted.[14]

which is a solution for the equation bx + c = dx + e equivalent to x = e − c/b − d, where rupas refers to the constants c and e. He further gave two equivalent solutions to the general quadratic equation

18.44. Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. [The result is] the middle [number].
18.45. Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminish that by half the unknown [and] divide [the remainder] by its square. [The result is] the unknown.[14]

which are, respectively, solutions for the equation ax2 + bx = c equivalent to,

{\displaystyle x={\frac {{\sqrt {4ac+b^{2}}}-b}{2a}}}

and

{\displaystyle x={\frac {{\sqrt {ac+{\tfrac {b^{2}}{4}}}}-{\tfrac {b}{2}}}{a}}.}

He went on to solve systems of simultaneous indeterminate equations stating that the desired variable must first be isolated, and then the equation must be divided by the desired variable's coefficient. In particular, he recommended using "the pulverizer" to solve equations with multiple unknowns.

18.51. Subtract the colors different from the first color. [The remainder] divided by the first [color's coefficient] is the measure of the first. [Terms] two by two [are] considered [when reduced to] similar divisors, [and so on] repeatedly. If there are many [colors], the pulverizer [is to be used].[14]

Like the algebra of Diophantus, the 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.[15] The extent of Greek influence on this syncopation, if any, is not known and it is possible that both Greek and Indian syncopation may be derived from a common Babylonian source.[15]

ArithmeticEdit

The four fundamental operations (addition, subtraction, multiplication, and division) were known to many cultures before Brahmagupta. This current system is based on the Hindu Arabic number system and first appeared in Brahmasphutasiddhanta. Brahmagupta describes the multiplication as thus “The multiplicand is repeated like a string 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”. [16][page needed] Indian arithmetic was known in Medieval Europe as "Modus Indoram" meaning method of the Indians. In Brahmasphutasiddhanta, multiplication was named Gomutrika. In the beginning of chapter twelve of his Brahmasphutasiddhanta, entitled Calculation, Brahmagupta details operations on fractions. 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. He then gives rules for dealing with five types of combinations of fractions: a/c + b/c; a/c × b/d; a/1 + b/d; a/c + b/d × a/c = a(d + b)/cd; and a/c − b/d × a/c = a(d − b)/cd.[17]

SeriesEdit

Brahmagupta then goes on to give the sum of the squares and cubes of the first n integers.

12.20. The sum of the squares is that [sum] multiplied by twice the [number of] step[s] increased by one [and] divided by three. The sum of the cubes is the square of that [sum] Piles of these with identical balls [can also be computed].[18]

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.[19]

He gives the sum of the squares of the first nnatural numbers as n(n + 1)(2n + 1)/6 and the sum of the cubes of the first n natural numbers as (n(n + 1)/2)2..

hope it helps you.. plz mark as brainliest..