Biography of brahmagupta theorem

In Brahmagupta devised and used a special case of the Newton—Stirling interpolation formula of the second-order to interpolate new values of the sine function from other values already tabulated. The earth on all its sides is the same; all people on the earth stand upright, and all heavy things fall down to the earth by a law of nature, for it is the nature of the earth to attract and to keep things, as it is the nature of water to flow If a thing wants to go deeper down than the earth, let it try.

The earth is the only low thing, and seeds always return to it, in whatever direction you may throw them away, and never rise upwards from the earth. The division was primarily about the application of mathematics to the physical world, rather than about the mathematics itself. In Brahmagupta's case, the disagreements stemmed largely from the choice of astronomical parameters and theories.

If the moon were above the sun, how would the power of waxing and waning, etc. The near half would always be bright. In the same way that the half seen by the sun of a pot standing in sunlight is bright, and the unseen half dark, so is [the illumination] of the moon [if it is] beneath the sun. The brightness is increased in the direction of the sun.

At the end of a bright [i. Hence, the elevation of the horns [of the crescent can be derived] from calculation. He explains that since the Moon is closer to the Earth than the Sun, the degree of the illuminated part of the Moon depends on the relative positions of the Sun and the Moon, and this can be computed from the size of the angle between the two bodies.

Further work exploring the longitudes of the planets, diurnal rotation, lunar and solar eclipses, risings and settings, the moon's crescent and conjunctions of the planets, are discussed in his treatise Khandakhadyaka. Contents move to sidebar hide. Article Talk. Read Edit View history. Tools Tools. Download as PDF Printable version.

Biography of brahmagupta theorem

In other projects. Wikimedia Commons Wikisource Wikidata item. This is the latest accepted revisionreviewed on 4 January Indian mathematician and astronomer — Rules for computing with Zero Modern numeral system Brahmagupta's theorem Brahmagupta's identity Brahmagupta's problem Brahmagupta—Fibonacci identity Brahmagupta's interpolation formula Brahmagupta's formula.

Life and career [ edit ]. Works [ edit ]. Reception [ edit ]. Mathematics [ edit ]. Algebra [ edit ]. Arithmetic [ edit ]. Squares and Cubes [ edit ]. Zero [ edit ]. Diophantine analysis [ edit ]. Pythagorean triplets [ edit ]. Pell's equation [ edit ]. Geometry [ edit ]. Brahmagupta's formula [ edit ]. Main article: Brahmagupta's formula. Triangles [ edit ].

Brahmagupta's theorem [ edit ]. Main article: Brahmagupta theorem. Pi [ edit ]. Measurements and constructions [ edit ]. Trigonometry [ edit ]. Sine table [ edit ]. Interpolation formula [ edit ]. Main article: Brahmagupta's interpolation formula. Early concept of gravity [ edit ]. Astronomy [ edit ]. See also [ edit ]. References [ edit ].

Notes [ edit ]. 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 biography of brahmagupta theorem 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 Brahmasphutasiddhantaa 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. Zero divided by zero is zero. Let us try to multiply by with the help of the gomutrika method.

Now multiply the of the top row by the 3 in the top position of the left-hand column. Now multiply the of the second row by the 1 in the left-hand column writing the number in the line below the but moving one place to the right. 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. 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 biography of brahmagupta theorem 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. We look below at some of the remarkable ideas which Brahmagupta's two treatises contain. 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.