Brahmagupta brief biography of abraham

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 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 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. 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. 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 a , b , c 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. The two [lower segments] of the two diagonals are two sides in a triangle; the base [of the quadrilateral is the base of the triangle]. Its perpendicular is the lower portion of the [central] perpendicular; the upper portion of the [central] perpendicular is half of the sum of the [sides] perpendiculars diminished by the lower [portion of the central perpendicular].

Many of these concepts are credited to Brahmagupta himself. Brahmagupta studied the writings of notable scholars like Aryabhata I, Pradyumna, Latadeva, Varahamihira, Srisena, Simha, and Vijayanandan, along with Vishnuchandra and the five traditional Indian astrological Siddhantas. His work, including the famous Brahmagupta formula, has made significant contributions to mathematics.

Brahmagupta was born in CE. He lived in Bhillamala, now Bhinmal, in Rajasthan, during the reign of the Chavda dynasty ruler, Vyagrahamukha. Brahmagupta, known as a Bhillamalacharya or the teacher from Bhillamala, was dedicated to discovering new concepts. Bhillamala was the capital of Gurjaradesa, a significant region in West India, which included parts of modern southern Rajasthan and northern Gujarat.

It was also a center for mathematics and astronomy studies. Brahmagupta studied the five classic Siddhantas of Indian astronomy and the works of other astronomers like Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin, and Vishnuchandra. At the age of 30, Brahmagupta authored the Brahmasphutasiddhanta , a revised version of the Siddhanta of the Brahmapaksha school of astronomy.

Brahmagupta book contains significant teachings in mathematics, including algebra, geometry, trigonometry, and algorithms, featuring new concepts credited to Brahmagupta himself. At 67, he wrote Khandakhadyaka, a practical guide to Indian astronomy for students. This Brahmagupta information highlights his contributions as a renowned Brahmagupta mathematician.

The Brahmagupta formula, which he developed, remains a significant part of his legacy. Brahmagupta, an influential Indian mathematician, established the properties of the number zero, which were crucial for the advancement of mathematics and science. Here are some key contributions by Brahmagupta:. Brahmagupta, a renowned Indian mathematician, made significant contributions to science and astrology.

He argued that the Earth and the universe are spherical, not flat. He was the first to use mathematics to predict the positions of planets and the timings of lunar and solar eclipses. These findings were major scientific advancements at the time. Brahmagupta also calculated the length of the solar year to be days, 5 minutes, and 19 seconds, very close to the current measurement of days, 5 hours, and 19 seconds.

At 30, Brahmagupta wrote his most famous work, the Brahmasphutasiddhanta, in AD. It includes many of his original studies and calculations. While much of the Brahmagupta books focuses on astronomy, it also covers a wide range of mathematical topics such as algorithms, trigonometry, geometry, and algebra. The book explains the importance of zero, rules for working with positive and negative numbers, and formulas for solving linear and quadratic equations.

Brahmagupta also reinforced his belief that the Earth is spherical, countering the prevalent flat Earth theory of his time. 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 work was the first to define how zero and negative integers should be used in calculations. This translation, known as the "Great Sindhind," had a profound impact on Islamic scholars such as al-Khwarizmi and al-Battani.

It played a significant role in the transmission of Indian mathematical and astronomical knowledge to the Islamic world.

Brahmagupta brief biography of abraham

Brahmagupta's contributions to astronomy and mathematics continue to be celebrated. He is credited with pioneering the use of algebra in astronomy, developing innovative methods for celestial computations, and advancing the understanding of the solar system. His legacy as a brilliant scholar and a visionary thinker endures among mathematicians and astronomers even today.

First let us give an overview of their contents. These ten chapters are arranged in topics which are typical of Indian mathematical astronomy texts of the period. The topics covered are: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; the moon's shadow; conjunctions of the planets with each other; and conjunctions of the planets with the fixed stars.

The remaining fifteen chapters seem to form a second work which is major addendum to the original treatise. The chapters are: examination of previous treatises on astronomy; on mathematics; additions to chapter 1 ; additions to chapter 2 ; additions to chapter 3 ; additions to chapter 4 and 5 ; additions to chapter 7 ; on algebra; on the gnomon; on meters; on the sphere; on instruments; summary of contents; versified tables.

Brahmagupta's understanding of the number systems went far beyond that of others of the period. He gave some properties as follows:- When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero. He also gives arithmetical rules in terms of fortunes positive numbers and debts negative numbers :- A debt minus zero is a debt.

A fortune minus zero is a fortune. Zero minus zero is a zero. A debt subtracted from zero is a fortune. A fortune subtracted from zero is a debt. The product of zero multiplied by a debt or fortune is zero. The product of zero multipliedby zero is zero.