Khandakhadyaka brahmagupta biography

Brahmagupta made many contributions to astronomy, including methods for calculating the positions of celestial bodies, their rise and set times, and the prediction of lunar and solar eclipses. Brahmagupta also challenged the Puranic belief in a flat Earth, observing instead that both the Earth and the sky are round and that the Earth is in motion.

Brahmagupta, an Indian mathematician and astronomer, made significant contributions to mathematics and astronomy. Here are some key achievements of Brahmagupta:. The achievements of Brahmagupta had a lasting influence on the study of mathematics and science in India and around the world. As a renowned Brahmagupta mathematician, his work continues to be celebrated for its impact on various scientific fields.

Brahmagupta, a pioneering Indian mathematician, introduced principles for mathematical operations involving zero and negative numbers in his book, Brahmasphutasiddhanta. This khandakhadyaka brahmagupta biography was the first to define how zero and negative integers should be used in calculations. Zero is a crucial concept in mathematics and is fundamental to our number system.

Brahmagupta mathematician laid the foundation for these concepts with his Brahmagupta formulahighlighting the significance of zero in mathematics. It is believed that Brahmagupta died between and CE, with many sources suggesting he lived until CE. Brahmagupta is considered one of the greatest Indian mathematicians of all time. His contributions to mathematics and science have had a significant impact, establishing fundamental rules that help solve many mathematical problems today.

The period around Brahmagupta death marks the end of a remarkable era of scientific advancement. Brahmagupta was referred to by Bhaskara II, his successor at Ujjain, as the 'ganak-chakra-churamani,' meaning the gem of the circle of mathematicians. Brahmagupta was the superintendent of the observatory in Ujjain, a major center for ancient Indian mathematical astrology.

Among Brahmagupta's books, the most well-known is the Brahmasphutasiddhanta, which covers both astronomy and mathematics. In chapter eighteen of his Brahmasphutasiddhanta, he provided a solution for the general linear equation. He also offered two equivalent solutions for the general quadratic equation. The Brahmasphutasiddhanta is the first book to outline rules for arithmetic operations involving zero and negative numbers.

His most famous geometric result is the Brahmagupta formula for calculating the area of cyclic quadrilaterals. He provided solutions for general linear and quadratic equations. His book, Brahmasphutasiddhanta, introduced rules for using zero and negative numbers in arithmetic. He is renowned for his geometric work, especially the Brahmagupta formula for cyclic quadrilaterals.

Brahmagupta's work also touched on the concept of gravity, explaining that bodies fall towards the Earth due to its attraction, similar to how water flows. Aryabhata, a renowned Indian mathematician and astronomer from the 5th century AD, made important contributions to the development of mathematical ideas, including the concept of zero.

While Brahmagupta later formalized the mathematical rules for zero, Aryabhata's work provided the foundation for these advancements. Skip to content Search for:. Table of Contents. Are you a Sri Chaitanya student? No Yes. Where was Brahmagupta born and when? Brahmagupta was born in AD in the town of Bhinmal, Rajasthan. What is Brahmagupta's other name?

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 khandakhadyaka brahmagupta biography 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 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 khandakhadyaka brahmagupta biographies, [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. 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.

Khandakhadyaka brahmagupta biography

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.

According to his statements in some received sources, Brahmagupta was born in CE. He resided in Bhillamalapresently Bhinmal, in Rajasthan, although during reign of the Chavda dynasty ruler, Vyagrahamukha. He was always focused to work finding new concepts. Later, commentators referred to him as a Bhillamalacharya or the instructor from Bhillamala.

It was also a centre of study institutions for mathematics and astronomy. Brahmagupta studied the five classic Siddhantas of Indian astronomy but also the learning of many other astronomers, including Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin, and Vishnuchandra. Somewhere at the age of 30, he authored and introduced the book named Brahmasphutasiddhanta, which itself is regarded to be a revised version of the recognised Siddhanta of the Brahmapaksha institution of astronomy.

The book includes important math teachings, including algebra, geometry, trigonometry, and algorithmics, all of which are claimed to include new concepts credited to Brahmagupta himself. At the age of 67, he authored Khandakhadyaka, a practical handbook of Indian astronomy, categorized within Karana, for students. Brahmagupta was harsh in his objections to competing astronomers, and his Brahmasphutasiddhanta represents one of the early internal divisions between many Indian mathematicians.

Disputes in Brahmagupta's case originated mostly from the selection of scientific factors and ideas. The selection was more concerned with applying mathematics to the physical world to discover or understand new concepts. Brahmagupta made a significant contribution to astronomy, including techniques for estimating the location of celestial bodies over a period, their emerging and setting, connectives, and the computation of lunar and solar eclipses.

Brahmagupta said that because the Moon is closer to the Ground than the sun, the khandakhadyaka brahmagupta biography of the lit section of the Moon is determined by the Sun's and Moon's relative positions, which can be calculated using the size of the separation between the two objects. In section eighteenth of Brahmasphutasiddhanta, Brahmagupta developed a solution to the generalized linear equation:.

The rupas are [subtracted on the side] below that from which the square and the unknown are to be subtracted. Here rupas denote the constant c and e. Moreover, the overall solution equals to below equation:. He answered processes of simultaneous indefinite equations first by isolating the chosen component but then just dividing the equation by the selected variable's coefficients.

Many cultures including Brahmagupta were aware of the four fundamental functions of addition, subtraction, multiplication, and division. The present system relied on the Hindu-Arabic number system and was originally used in the Brahmasphutasiddhanta. Brahmagupta described the four different multiplication approaches in his book. One of those four approaches, named gom?

Brahmagupta also determined the combination of the squares and cubes of first n numbers. During this determination, Brahmagupta found the answer in terms of the sum of first n integers, instead of n, as is common nowadays. The Brahmasphutasiddhanta of Brahmagupta was the very first publication to establish principles for mathematical operations with zero and negative integers.

The Brahmasphutasiddhanta is considered the first recognized literature to regard zero as a figure in and of itself, instead of as a placeholder digit in expressing another number, as the Babylonians did, or as a sign for lack of amount, as Ptolemy and the Romans did. However, he stated that if any type of value numeric is divided by zero, it yields the total zero.

Brahmagupta discovered the qualities of the digit 0, which became critical for the development of math and science. Ifrah translates "gomutrika" to "like the trajectory of a cow's urine". Consider the khandakhadyaka brahmagupta biography of multiplied by We begin by setting out the sum as follows: 2 6 4 References show. Biography in Encyclopaedia Britannica.

G Ifrah, A universal history of numbers : From prehistory to the invention of the computer London, S S Prakash Sarasvati, A critical study of Brahmagupta and his works : The most distinguished Indian astronomer and mathematician of the sixth century A. Delhi, G S Bhalla, Brahmagupta's quadrilateral, Math. History Sci. B Datta, Brahmagupta, Bull.

Calcutta Math. XII Wiesbaden,83 - R C Gupta, Brahmagupta's formulas for the area and diagonals of a cyclic quadrilateral, Math.