Image of brahmagupta the mathematician who cracked

Brahmagupta had many discrepancies with his fellow mathematicians and most of the chapters of this book talked about the loopholes in their theories. It had many rules of arithmetic which is part of the mathematical solutions now.

Image of brahmagupta the mathematician who cracked: Brahmagupta (c. – c. CE) was

Brahmagupta was the one to give the area of a triangle and the important rules of trigonometry such as values of the sin function. He introduced the formula for cyclic quadrilaterals. Additionally he introduced the concept of negative numbers. Brahmagupta argued that the Earth and the universe are round and not flat. He was the first to use mathematics to predict the positions of the planets, the timings of the lunar and solar eclipses.

Though all this seems like obvious and simple solutions it was a major improvement in science at that time. Aryabhatt used letters of the alphabet to denote numbers and the zero. It was Brahmagupt who first used zero as a number besides introducing rules dealing with it. Facebook Comments Box. The following two tabs change content below.

Bio Latest Posts. Latest posts by manoshi sinha see all. Contact Us info myindiamyglory. Now multiply the of the third row by the 5 in the left-hand column writing the number in the line below the but moving one place to the right. The second form of this method requires, first writing the second number on the right but with the order of the digits reversed as follows.

Image of brahmagupta the mathematician who cracked: Brahmagupta was a mathematician and

In the third variant of this method, just write each number once but otherwise follows the second method. According to Majumdar, Brahmgupta used continued fractions to solve such equations. A sample of the types of problem solved by him is Five hundred drammas were loaned at an unknown rate of interest, The interest on the money for four months was loaned to another at the same rate of interest and amounted in ten mounths to 78 drammas.

Give the rate of interest. He gave the sum of, a series of cubes and a series of squares for the first n natural numbers as follows:. He mentioned. 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 d, a, b and c. A Pythagorean triple can therefore be obtained from a, b and c by multiplying each of them by the least common multiple of their denominators. Given the sides of a cyclic quadrilateral, he provided an approximate and exact formula for the area of the cyclic quadrilateral. 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. The court of Caliph Al-Mansur — received an embassy from Sindh, including an astrologer called Kanaka, who brought possibly memorised astronomical texts, including those of Brahmagupta. An immediate outcome was the spread of the decimal number system used in the texts.

The mathematician Al-Khwarizmi — CE wrote a text called al-Jam wal-tafriq bi hisal-al-Hind Addition and Subtraction in Indian Arithmeticwhich was translated into Latin in the 13th century as Algorithmi de numero indorum. Through these texts, the decimal number system and Brahmagupta's algorithms for arithmetic have spread throughout the world.

Al-Khwarizmi also wrote his own version of Sindhinddrawing on Al-Fazari's version and incorporating Ptolemaic elements. Indian astronomic material circulated widely for centuries, even making its way into medieval Latin texts. The historian of science George Sarton called Brahmagupta "one of the greatest scientists of his race and the greatest of his time.

The difference between rupaswhen inverted and divided by the difference of the [coefficients] 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. He further gave two equivalent solutions to the general quadratic equation. 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.

Whatever is the square-root of the rupas multiplied by the square [and] increased by the square of half the unknown, diminished that by half the unknown [and] divide [the remainder] by its square. 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. Subtract the colors different from the first color. If there are many [colors], the pulverizer [is to be used]. 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.

Image of brahmagupta the mathematician who cracked: Brahmagupta (– CE). Brahmagupta, a

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 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. 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. 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 zero. 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. The key to his solution was the identity, [ 29 ].

Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals.