biography of brahmagupta in 300 words

 MacTutor

Brahmagupta.

When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.

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. The product or quotient of two fortunes is one fortune. The product or quotient of two debts is one fortune. The product or quotient of a debt and a fortune is a debt. The product or quotient of a fortune and a debt is a debt.

Positive or negative numbers when divided by zero is a fraction the zero as denominator. Zero divided by negative or positive numbers is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.

Brahmagupta perhaps used the method of continued fractions to find the integral solution of an indeterminate equation of the type a x + c = b y ax + c = by a x + c = b y .

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.

References ( show )

• D Pingree, Biography in Dictionary of Scientific Biography ( New York 1970 - 1990) . See THIS LINK .
• Biography in Encyclopaedia Britannica. http://www.britannica.com/biography/Brahmagupta
• H T Colebrooke, Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhaskara (1817) .
• G Ifrah, A universal history of numbers : From prehistory to the invention of the computer ( London, 1998) .
• S S Prakash Sarasvati, A critical study of Brahmagupta and his works : The most distinguished Indian astronomer and mathematician of the sixth century A.D. ( Delhi, 1986) .
• S P Arya, On the Brahmagupta- Bhaskara equation, Math. Ed. 8 (1) (1991) , 23 - 27 .
• G S Bhalla, Brahmagupta's quadrilateral, Math. Comput. Ed. 20 (3) (1986) , 191 - 196 .
• B Chatterjee, Al-Biruni and Brahmagupta, Indian J. History Sci. 10 (2) (1975) , 161 - 165 .
• B Datta, Brahmagupta, Bull. Calcutta Math. Soc. 22 (1930) , 39 - 51 .
• K Elfering, Die negativen Zahlen und die Rechenregeln mit ihnen bei Brahmagupta, in Mathemata, Boethius Texte Abh. Gesch. Exakt. Wissensch. XII ( Wiesbaden, 1985 , 83 - 86 .
• R C Gupta, Brahmagupta's formulas for the area and diagonals of a cyclic quadrilateral, Math. Education 8 (1974) , B 33 -B 36 .
• R C Gupta, Brahmagupta's rule for the volume of frustum-like solids, Math. Education 6 (1972) , B 117 -B 120 .
• R C Gupta, Munisvara's modification of Brahmagupta's rule for second order interpolation, Indian J. Hist. Sci. 14 (1) (1979) , 66 - 72 .
• S Jha, A critical study on 'Brahmagupta and Mahaviracharya and their contributions in the field of mathematics', Math. Ed. ( Siwan ) 12 (4) (1978) , 66 - 69 .
• S C Kak, The Brahmagupta algorithm for square rooting, Ganita Bharati 11 (1 - 4) (1989) , 27 - 29 .
• T Kusuba, Brahmagupta's sutras on tri- and quadrilaterals, Historia Sci. 21 (1981) , 43 - 55 .
• P K Majumdar, A rationale of Brahmagupta's method of solving ax + c = by, Indian J. Hist. Sci. 16 (2) (1981) , 111 - 117 .
• J Pottage, The mensuration of quadrilaterals and the generation of Pythagorean triads : a mathematical, heuristical and historical study with special reference to Brahmagupta's rules, Arch. History Exact Sci. 12 (1974) , 299 - 354 .
• E R Suryanarayan, The Brahmagupta polynomials, Fibonacci Quart. 34 (1) (1996) , 30 - 39 .

Additional Resources ( show )

Other pages about Brahmagupta:

• See Brahmagupta on a timeline
• Astronomy: The Structure of the Solar System
• Heinz Klaus Strick biography

Other websites about Brahmagupta:

• Dictionary of Scientific Biography
• Encyclopaedia Britannica
• MathSciNet Author profile

Honours ( show )

Honours awarded to Brahmagupta

• Popular biographies list Number 4

Cross-references ( show )

• History Topics: A chronology of π
• History Topics: A history of Zero
• History Topics: An overview of Indian mathematics
• History Topics: Infinity
• History Topics: Pell's equation
• History Topics: Quadratic, cubic and quartic equations
• History Topics: The Arabic numeral system
• History Topics: The trigonometric functions
• Student Projects: Indian Mathematics - Redressing the balance: Chapter 10
• Student Projects: Indian Mathematics - Redressing the balance: Chapter 11
• Student Projects: Indian Mathematics - Redressing the balance: Chapter 12
• Student Projects: Indian Mathematics - Redressing the balance: Chapter 13
• Student Projects: Indian Mathematics - Redressing the balance: Chapter 14
• Student Projects: Indian Mathematics - Redressing the balance: Chapter 17
• Other: 2009 Most popular biographies
• Other: Earliest Known Uses of Some of the Words of Mathematics (N)
• Other: Earliest Known Uses of Some of the Words of Mathematics (R)
• Other: Earliest Uses of Symbols for Fractions
• Other: Most popular biographies – 2024
• Other: Popular biographies 2018
• Other: The Structure of the Solar System

Brahmagupta | Great Indian Mathematician

Table of contents.

22 September 2020                

Read time: 3 minutes

Introduction

In India, it is second nature to consult an astrologer who suggests an auspicious time of Muhurat for an important event. In other words, Astrology and Astronomy is a part of our life. Our calendar both the solar and the lunar calendar accurately calculate the festivals, moon phases, eclipses and many other happenings in not just our solar system, but also the cosmos or the Universe. What is impressive is that our ancient Astronomers and Astrologers used mathematics to calculate the auspicious timing for important events in our life.

One thing our ancient scientists were aware of was that there is an order/ logic in this huge expanse and vastness. It is this realization that led to the discoveries in Mathematics.

Who is Brahmagupta?

Brahmagupta ( 597- 668AD) was one such genius Astronomer - Mathematician. His father Jisnugupta was an Astrologer in the city of Bhinmal ( Rajasthan). Brahmagupta too considered himself an Astronomer however today he is remembered for his huge contributions to the field of Mathematics. By his admission, he did Mathematics or solved problems for pleasure!

Ujjain was the centre of Ancient Indian mathematical astronomy. Brahmagupta was the director of this centre. Brahmagupta wrote many textbooks for mathematics and astronomy while he was in Ujjain. These include ‘Durkeamynarda’ (672), ‘Khandakhadyaka’ (665), ‘Brahmasphutasiddhanta’ (628) and ‘Cadamakela’ (624). The ‘Brahmasphutasiddhanta’ meaning the ‘Corrected Treatise of Brahma’ is one of his well-known works.

Works of Brahmagupta

Brahmagupta, like all scholars in those times, wrote in elliptical verse.

Brahmasphutasiddhanta ((Brahma’s Correct System of Astronomy, or The Opening of the Universe.) written in 628 was his most famous work. This book has twenty-five chapters and a total of 1008 stanzas. Historians believe that the first ten were originally written by Brahmagupta because they are arranged like the typical mathematical astronomy texts in that period. It covers 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 a major addendum to the original treatise.

Brahmasphutasiddhanta is the earliest known text that treated zero as a number. The Greeks and Romans merely used symbols, and the Babylonians used a shell to represent nothing.

He gave the concept of positive numbers which he called wealth or dhan and negative numbers which he called debt or ऋण

 He wrote the rules as follows:

This was a revolution as most people dismissed the possibility of a negative number thereby proving that quadratic equations (of the type \(\rm{}x2 + 2 = 11,\) for example) could, in theory, have two possible solutions, one of which could be negative, because \(32 = 9\) and \(-32 = 9\) . Brahmagupta went yet further by considering systems of simultaneous equations (set of equations containing multiple variables) and solving quadratic equations with two variables

An example from Brahmasphutasiddhanta

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 months to \(78\) drammas. Give the rate of interest.

  Brahmagupta Formula

Brahmagupta found the formula for cyclic quadrilaterals though he did not focus on the cyclic character of the figure. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and an exact formula for the figure's area.

His second book The Khandakhadyaka - 665 AD has eight chapters. This book too details longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; and conjunctions of the planets.

What stands out as a mathematical genius in this work is the interpolation formula he uses to compute values of sines.

Brahmagupta achievements

Brahmagupta defined the properties of the number zero, which was crucial for the future of mathematics and science. Brahmagupta enumerated the properties of zero as:

   ★ When a number is subtracted from itself, we get a zero

   ★ Any number divided by zero will have the answer as zero

   ★ Zero divided by zero is equal to zero

Discovered the formula to solve quadratic equations.

Discovered the value of pi ( 3.162….) almost accurately. He put the value 0.66% higher than the true value. ( 3.14)

With calculations, he indicated that Earth is nearer to the moon than the sun.

Found a formula to calculate the area of any four-sided figure whose corners touch the inside of a circle.

Calculated the length of a year is 365 days 6 hours 12 minutes 9 seconds.

Brahmagupta talked about ‘gravity.’ To quote him, ‘Bodies fall towards the earth as it is in the nature of the earth to attract bodies, just as it is in the nature of water to flow.’

Proved that the Earth is a sphere and calculated its circumference to be around 36,000 km (22,500 miles).

Brahmagupta established rules for working with positive and negative numbers, such as:

  Ø Negative \(+\) Negative number \(=\) Negative number

  Ø Subtracting a Negative from a positive number is the same as adding the two numbers.

  Ø Negative X Negative number \(=\) Positive number.

  Ø Positive number ÷ Negative number \(=\) Negative number.

Indian philosophy reiterates that we are a small part of a Brahmand, the cosmos or the universe. This humbling knowledge was perhaps the basis of the concept of a zero or a void because it came from a culture that conceived and acknowledged the idea of the infinite. A symbol \((0)\) denoting “nothing” was a part of Indian culture. This becomes particularly relevant as it indicates a vibrant, philosophical culture that recognised the power of nothingness and thus actually recognised the power of Mathematics and its role in the order of nothingness.

Although Brahmagupta thought of himself as an astronomer who did some mathematics, he is now mainly remembered for his contributions to mathematics. He was honoured by the title given to him by a fellow scientist ‘ Ganita Chakra Chudamani’ which is translated as ‘The gem of the circle of mathematicians’.

Frequently Asked Questions (FAQs)

What did brahmagupta discover.

Brahmadutta has a lot to his credit:

• Brahmagupta gave the solution of the general linear equation in chapter eighteen of Brahmasphutasiddhānta.
• He gave two equivalent solutions to the general quadratic equation.
• Brahmagupta's Brahmasphuṭasiddhānta is the first book that provides rules for arithmetic manipulations that apply to zero and to negative numbers.
• Brahmagupta's most famous result in geometry is his formula for cyclic quadrilaterals.

Where was brahmagupta born?

Brahmagupta was born in the city of Bhinmal, Rajasthan.

When was brahmagupta born?

Brahmagupta was born in 597 AD.

When did brahmagupta die?

Brahmagupta passed away in 668 AD.

• Mathematicians
• Math Lessons
• Square Roots
• Math Calculators
• Brahmagupta: Mathematician and Astronomer

BRAHMAGUPTA: MATHEMATICIAN AND ASTRONOMER

The great 7th Century Indian mathematician and astronomer Brahmagupta wrote some important works on both mathematics and astronomy. He was from the state of Rajasthan of northwest India (he is often referred to as Bhillamalacarya, the teacher from Bhillamala), and later became the head of the astronomical observatory at Ujjain in central India. Most of his works are composed in elliptic verse, a common practice in Indian mathematics at the time, and consequently have something of a poetic ring to them.

It seems likely that Brahmagupta’s works, especially his most famous text, the “Brahmasphutasiddhanta”, were brought by the 8th Century Abbasid caliph Al-Mansur to his newly founded centre of learning at Baghdad on the banks of the Tigris, providing an important link between Indian mathematics and astronomy and the nascent upsurge in science and mathematics in the Islamic world .

In his work on arithmetic, Brahmagupta explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots. He also gave rules for dealing with five types of combinations of fractions. He gave the sum of the squares of the first n natural numbers as n ( n + 1)(2 n + 1) ⁄ 6 and the sum of the cubes of the first n natural numbers as ( n ( n + 1) ⁄ 2 ) ² .

Brahmasphutasiddhanta – Treat Zero as a Number 

Brahmagupta’s genius, though, came in his treatment of the concept of (then relatively new) the number zero. Although often also attributed to the 7th Century Indian mathematician Bhaskara I, his “Brahmasphutasiddhanta” is probably the earliest known text to treat zero as a number in its own right, rather than as simply a placeholder digit as was done by the Babylonians , or as a symbol for a lack of quantity as was done by the Greeks and Romans .

Brahmagupta established the basic mathematical rules for dealing with zero (1 + 0 = 1; 1 – 0 = 1; and 1 x 0 = 0), although his understanding of division by zero was incomplete (he thought that 1 ÷ 0 = 0). Almost 500 years later, in the 12th Century, another Indian mathematician, Bhaskara II, showed that the answer should be infinity, not zero (on the grounds that 1 can be divided into an infinite number of pieces of size zero), an answer that was considered correct for centuries. However, this logic does not explain why 2 ÷ 0, 7 ÷ 0, etc, should also be zero – the modern view is that a number divided by zero is actually “undefined” (i.e. it doesn’t make sense).

Brahmagupta’s view of numbers as abstract entities, rather than just for counting and measuring, allowed him to make yet another huge conceptual leap which would have profound consequence for future mathematics. Previously, the sum 3 – 4, for example, was considered to be either meaningless or, at best, just zero. Brahmagupta, however, realized that there could be such a thing as a negative number, which he referred to as “debt” as a opposed to “property”. He expounded on the rules for dealing with negative numbers (e.g. a negative times a negative is a positive, a negative times a positive is a negative, etc).

Furthermore, he pointed out, quadratic equations (of the type x 2 + 2 = 11, for example) could in theory have two possible solutions, one of which could be negative, because 3 2 = 9 and -3 2 = 9. In addition to his work on solutions to general linear equations and quadratic equations, Brahmagupta went yet further by considering systems of simultaneous equations (set of equations containing multiple variables), and solving quadratic equations with two unknowns, something which was not even considered in the West until a thousand years later, when Fermat was considering similar problems in 1657.

Brahmagupta’s Theorem on cyclic quadrilaterals

Brahmagupta even attempted to write down these rather abstract concepts, using the initials of the names of colours to represent unknowns in his equations, one of the earliest intimations of what we now know as algebra.

Brahmagupta dedicated a substantial portion of his work to geometry and trigonometry. He established √10 (3.162277) as a good practical approximation for π (3.141593), and gave a formula, now known as Brahmagupta’s Formula, for the area of a cyclic quadrilateral, as well as a celebrated theorem on the diagonals of a cyclic quadrilateral, usually referred to as Brahmagupta’s Theorem.

Famous Mathematicians

List and Biographies of Great Mathematicians

Brahmagupta

According to himself, Brahmagupta was born in 598 CE and was the follower of Shaivism. During the rule of Chapa dynasty ruler, Vyagrahamukha, he lived in Bhillamala according to historian, yet there is no conclusive proof of that. Other sociologists believed he might have belonged to Multan region. Bhillamala was the capital of Gurjaradesa, currently known as Gujrat. It was the hub of all mathematical and astronomical learning. Bharmagupta assumed the position of an astronomer at Brahmapaksha school.

At a young age of 30, he wrote the improved treatise of Brahma called Brāhmasphuṭasiddhānta . It is speculated that it was the revision of the siddhanta he received from the school. He brought originality to the treatise by adding a great deal of new material to it. The book is written in arya-meter comprising 1008 verses and 24 chapters. An enormous amount of material is found on astronomy, while it also includes chapters on mathematics, trigonometry, algorithms and algebra.

After completing his work in Bhillamala, he moved to Ujjain which was also considered a chief location with respect to studies in astronomy. Aside from his revision of Brahma treatise, at the mature age of 67, he wrote another foremost work in mathematics entitled, Khanda-khādyaka . This text is a practical manual of Indian astronomy which is meant to guide students.

In his Brahma treatise, Brahmagupta criticized contemporary Indian astronomer on their different opinion. The rift between the mathematicians was created based on their varying ways of applying mathematics to physical world. Brahma had different views on astronomical parameters and theories. In his books he dedicated several chapters critiquing mathematical theories and their application.

There are numerous science historians who made testimony to his great scientific contribution. According to George Sarton, he was a great scientist of his race. In Medieval Europe Indian arithmetic was called “Modus Indoram” which means method of the Indians. He called multiplication gomutrika in his Brahmasphutasiddhanta . His work was further explored by Bhāskara II who held Brahmagupta at an elevated position for his immense contribution to mathematics. His work was further simplified and added illustrations to by Prithudaka Svamin. In addition to that his work was commented upon by Lalla and Bhattotpala in the eighth and ninth century. When Sindh was conquered by Arabs, his work was translated into Arabic by an astronomer, Muhammad al-Fazari which led to the use of decimal number system in written discourse.

Some of the major contribution to the field of astronomy by Brahmagupta are solar and lunar eclipse calculations and methods for calculating the position of heavenly bodies over time. Moreover, in a chapter titled Lunar Cresent he criticized the notion that the Moon is farther from the Earth than the Sun which was mentioned in Vedic scripture. He was of the view that the Moon is closer to the Earth than the Sun based on its power of waxing and waning. The illumination of the moon depends on the position and angle of Sunlight that hits the surface of the moon.

Brahmagupta Biography

Brahmagupta, an ancient Indian astronomer and mathematician, is best known for his groundbreaking work in the field of astronomy. His treatise, ‘Brāhmasphuṭasiddhānta’, not only had a profound impact on the development of astronomy in India but also influenced Islamic mathematics and astronomy. Despite being an orthodox Hindu, he was ahead of his time in realizing that the Earth is a sphere. Additionally, he was a highly revered mathematician and his book was the first to mention zero as a number and provide rules for its use with negative and positive numbers.

Quick Facts

• Died At Age: 72
• Died on: 670
• Astronomers
• Mathematicians

Childhood & Early Life

Brahmagupta was born in 598 AD into an orthodox Shaivite Hindu family. His father’s name was Jishnugupta. It is generally believed that he was born in Ujjain. Not much is known about his early life.

Education and Career

As a young man, Brahmagupta studied astronomy extensively. He was well-read in the five traditional siddhanthas on Indian astronomy, and also studied the work of other ancient astronomers such as Aryabhata I, Latadeva, Pradyumna, Varahamihira, Simha, Srisena, Vijayanandin, and Vishnuchandra. He became an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during his era.

Later Years

Brahmagupta is believed to have lived and worked in Bhinmal in present-day Rajasthan, India, for a few years. The city was a center of learning for mathematics and astronomy, and he flourished as an astronomer in the intellectual atmosphere of the city.

At the age of 30, he composed the theoretical treatise ‘Brāhmasphuṭasiddhānta’ (“Correctly established doctrine of Brahma”) in 628 AD. The work is thought to be a revised version of the received siddhanta of the Brahmapaksha school, incorporated with some of his own new material. Primarily a book of astronomy, it also contains several chapters on mathematics.

Contributions

Brahmagupta is credited with giving the most accurate early calculations of the length of the solar year. He also introduced new methods for solving quadratic equations and gave equations to solve systems of simultaneous indeterminate equations. In addition, he provided a formula useful for generating Pythagorean triples and gave a recurrence relation for generating solutions to certain instances of Diophantine equations.

In mathematics, his contribution to geometry was especially significant. He gave formulas for the lengths and areas of various geometric figures, and his formula for cyclic quadrilaterals, now known as Brahmagupta’s formula, provides a way of calculating the area of any cyclic quadrilateral given the lengths of the sides.

Major Works

Brahmagupta’s treatise ‘Brāhmasphuṭasiddhānta’ is one of the first mathematical books to provide concrete ideas on positive numbers, negative numbers, and zero. The text also elaborated on the methods of solving linear and quadratic equations, rules for summing series, and a method for computing square roots. It also contained the first clear description of the quadratic formula.

One of his later works was the treatise ‘Khaṇḍakhādyaka’ (meaning “edible bite; morsel of food”), written in 665 AD, which covered several topics on astronomy.

Personal Life & Legacy

The details regarding Brahmagupta’s family life are obscure. He is believed to have died sometime after 665 AD.

Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

Brahmagupta

Apparently there is some discrepancy as to the possibility that Brahmagupta might have been born in Bhillamala; But it is a for a surety that he grew up in that city. He practiced the Hindu religion of Shaivite. This religion was more about how they projected themselves to their god, rather than following strict adherence to Hinduism tenets.

A final note about his birthplace is that there was even one consideration he came from the Abu region in India. Even though his birthplace may be in question; there is no question as to his place in mathematical history.

Studies and Discoveries

Brahmagupta loved the studies of the heavens and became an astronomer of one of four major Indian astronomy schools; the Brahmapaksha. His studies followed some of the notables in Indian astronomy such as Varahmihara, Aryabhata and Simha. These and other names in the Indian astronomy world were indicative of the focus that Brahmagupta found most interesting.

The young Indian’s passion for astronomy took a backseat to nothing of his day. He absorbed himself in learning all he could about the subject. There were five siddhanthas on the topic of Indian astronomy and Brahmagupta was well versed on all of them in a short period of time.

Brahmagupta was a well versed writer in areas of astronomy and mathematics. However, his work did not treat them as separate subjects; he played the two together considerably in much of his work.

Through his research, he postulated a number of concepts that far surpassed many scholars in the arena of movement in the sky. He had established sound cycle motions of planetary motion across the sky and could accurately predict where they would rise and fall in the occurrence of each day.

Another area in astronomy that Brahmagupta excelled was in establishing clearer thought on the area of eclipses. For many cultures, the concept of the sun being blocked by the moon or alignment ideas was a spiritual matter.

Where the Indian astronomer came in was to design computations that accurately dated eclipse happenings. His work in this arena caused many to look at the young mathematician with greater respect.

When Brahmagupta was 30 years of age, he wrote his first work which was a revised look at Brahma astronomy. Entitled Brāhmasphuṭasiddhānta, the 25-chapter manuscript looked at standard topics of period mathematical astronomy that was part of the Indian study.

These chapters dealt with lunar and solar eclipses, longitudes of planets (both true and mean), shadowing of the moon and other areas of interest. These chapters seemed to be a repeat of what was considered to be known and simply restated.

The remaining chapters appeared to be a re-look at the viewed ideas and even believed to be refutations of some of the work. His purpose was not necessarily to debunk prior scholars, but to add original ideas on aspects of celestial concepts.

His treatise considers more in the use of accurate examples of geometry, algebra, trigonometry to answer some of the questions that plagued astronomers for centuries. His take on things was a challenge to the siddhanta he has received in his earlier learning.

It should be noted that Brahmagupta’s postulations into the movement in the heavens considered the earth to be a stationary body. (There is a belief that Brahmagupta may have purposely held to the stationary earth idea to save his own life.

The religion of the time held to the concept of the earth did not move as the earth was the center of all things.) Although his work articulated that motion was occurring with other planets and stars; everything hinged on this planet being a static position.

In this book he sets forth the concept that one year equals 365 days, six hours, five minutes and 19 seconds. In the second book, to be discussed, he adds seven minutes to the idea; similar to that of Indian astronomer and mathematician Aryabhata.

A couple points of note about math in this first of his works. In one chapter, Brahmagupta creates a beginning for the mindset of arithmetic. He discusses the Indian math of “pati-ganita” or “mathematics of procedures”.

Because the man had a deep passion of mathematics as a whole, this chapter seems to be an expose of himself in his love. He is frank about practical math and operations. It was sort of the math to the populace, or a look at “practical math”.

He relates that this math had to be a part of a mathematician. Another chapter detailed the work involved in algebra. Although the name itself did not exist, Brahmagupta gives great detail to area itself for what became our view of algebraic equations.

Brahmagupta’s work with mathematics, including algorithms, in the area of astronomy opened up new frontiers for astronomers to follow. More than that, it seemed to open up the man himself to his peers. This was not to be his last publication.

One of Brahmagupta’s career positions was to become the lead (modern day position of director) over the astronomy observatory in his hometown of Ujjain. Prior directors had been notables of the day and had established a huge reputation for the observatory. It seemed to fit that Brahmagupta would continue the outstanding work that came from that institution.

Though there is no basis as to verify that his first book affected the Islamic look at math and astronomy, there is a good chance that it did. Some felt that his first treatise impressed the scholars in the learning center of Baghdad and may have obtained a copy of the mathematical astronomy publication.

Then King Khalif Abbasid al-Mansoor is said to have requested the presence of a student of Brahmagupta’s teachings of astronomy to come give lectures. Translated into Arabic, the works of Brahmagupta would influence much of Arabic mathematical understanding.

This affect upon the math and sciences of the Middle East made its way to influence much of the same disciplines of Europe. The ancient world’s look at mathematics, via the realm of Brahmagupta’s involvement, impacted a considerable amount upon the western culture.

Another work that Brahmagupta published occurred when he was in his mid-60’s. Approximately in 665 he developed the treatise called Khandakhadyaka.

This work was considered to be done in response to the work of one of Brahmagupta’s fellow scholars, Aryabhata who wrote Ardharatrikapaksa . Aryahata was considered to be one that stipulated that each day began with the midnight hour.

Khandakhadyaka is made up of 8 chapters. These chapters look many of the same topics found in the first, such as eclipses, planet risings and settings, planet conjunctions and other ideas. Once again this seemed to be an attempt to enhance some of the ideas as put out by Aryabhata.

This second work also paid an even closer look at mathematics in general. It puts a deeper emphasis on computing values that involved sines. Thirty years later Brahmagupta still researches and continues to improve his work with geometry and algebra.

He is one of the first in the realm of mathematics to use story problems to showcase his ideas. Without going into the actual story verbatim, Brahmagupta uses the idea loaning money to one entity and then some to another. The finish was to come up with the rate of interest on the monies distributed.

There is considerable in modern mathematics that can be traced back to the work of Brahmagupta. One such method was in solving quadratic equations. Brahmagupta came up with a theorem (named after him) for figuring out the area of cyclic quadrilateral. This included figuring diagonal lengths as well.

Ancient math, such as geometry and trigonometry, had remained a constant in many ways up to the time of Brahmagupta.

He had a tenacity for delving into the research of commonly known equations and breaking them down to see if they were accurate. Over time this man would develop ideas that challenged and built upon the former ideas; similar to how he looked at mathematical astronomy.

The most notable innovations that Brahmagupta is remembered for is his look and pursuit of the number zero. Until this time, the zero had not been thought of as a number.

The formation of the zero shape was a commonplace consideration; as was the concept of the value of places (numerical placement) to form importance to numbers. These had pre-dated Brahmagupta and were considerations from the ancient world.

But it was Brahmagupta that established rules that put zero into the spotlight. He formulated equations that allowed zero to be used in positives and negatives.

Although he did not use those specific words, Brahmagupta did follow with the importance in the need of the zero placement. Without the use of zero and its value defined, according to him, arithmetic really had nowhere to go.

When it came to the zero, the Indian mathematician even enhanced the knowledge of zero in relation to multiplication. When it came to division he seemed to have incorrect assumptions established. But, it cannot be denied that Brahmagupta brought to the world of arithmetic the value and need for a neutral digit that was zero.

Brahmagupta’s Look at Zero listed:

• 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.
• 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.
• The product or quotient of two fortunes is one fortune.
• The product or quotient of two debts is one fortune.
• The product or quotient of a debt and a fortune is a debt.
• The product or quotient of a fortune and a debt is a debt.

The belief that the earth was flat as a pancake was a predominate belief in the ancient world; even into the middle ages. Although he was incorrect in his belief that the sun moved around the earth, since the earth had to be static in its existence; Brahmagupta was correct in giving a circular shape to the planet.

Other Insights of Brahmagupta

• The earth had a circumference of approximately 22,500 miles.
• Gave a close parameter to what pi is known to be as 3 or 3.16 if the measurement of a circle’s circumference to diameter ration needed to be more precise.
• Positive and negative numbers rule:
• When a negative number is subtracted from a positive; it is the same as adding two positive numbers. (2- -3=5; 2+3=5)
• Adding two negative numbers results in a negative number.
• Multiplying two negatives is same as multiplying two positive numbers.
• dividing a positive number by a negative, or a negative number by a positive result in a negative number.

Brahmagupta passed away in approximately 670. It appears part of his life’s work was a struggle between the Hindu religion and his own scientific mind’s research into astronomy from a mathematician’s perspective.

Brahmagupta cannot be denied his place in establishing much of contemporary work. For example, his teachings of the property “zero” influenced work in modern thermodynamics. Brahmagupta in some ways was a man born out of time in the way he looked at early math and astronomy.

One of his quotes accurately portrays who he was. “As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of the people if he proposes algebraic problems, and still more if he solves them.” F Cajori, “ A History of Mathematics”

Ancient India’s Brahmagupta: Pioneering the Foundations of Mathematics and Astronomy

• Post author By Mala Chandrashekhar
• Post date October 13, 2023
• No Comments on Ancient India’s Brahmagupta: Pioneering the Foundations of Mathematics and Astronomy

Introduction

In the annals of history, there are individuals whose contributions shape the course of human knowledge. Brahmagupta, an Indian mathematician and astronomer who lived during the 7th century CE, was one such luminary. His groundbreaking works, the “Brāhmasphuṭasiddhānta” and the “Khaṇḍakhādyaka,” not only revolutionized the fields of mathematics and astronomy but also laid the groundwork for countless future discoveries. In this blog post, we will delve into the life and accomplishments of Brahmagupta, highlighting his pioneering insights into gravity.

Brahmagupta: A Brief Biography

Born around 598 CE in the ancient city of Ujjain, Brahmagupta belonged to a lineage of esteemed mathematicians and astronomers. His father, Jisnugupta, was also a mathematician, and it is likely that Brahmagupta inherited his passion for these disciplines from his family. Brahmagupta’s genius became evident at a young age, and he made his mark as a prominent mathematician during the Gupta dynasty in India.

The Brāhmasphuṭasiddhānta: A Theoretical Masterpiece

In 628 CE, Brahmagupta authored his most renowned work, the “Brāhmasphuṭasiddhānta,” which translates to the “correctly established doctrine of Brahma.” This monumental text, consisting of 24 chapters, encompasses a wide range of mathematical and astronomical concepts. It was a significant departure from earlier works, as Brahmagupta introduced innovative ideas and theories that would influence scholars for centuries to come.

One of his most notable contributions was his description of gravity as an attractive force. In this groundbreaking insight, Brahmagupta used the Sanskrit term “gurutvākarṣaṇam (गुरुत्वाकर्षणम्)” to articulate this concept. This was a remarkable precursor to Isaac Newton’s universal law of gravitation, which would not be formulated until over a millennium later.

Brahmagupta’s work on algebra was equally pioneering. He introduced the rules for performing arithmetic operations with both positive and negative numbers, including zero. These foundational concepts were instrumental in shaping the development of algebraic notation and paved the way for future mathematical advances.

The Khaṇḍakhādyaka: A Practical Guide

Following the success of the “Brāhmasphuṭasiddhānta,” Brahmagupta continued to contribute to mathematics and astronomy. In 665 CE, he penned the “Khaṇḍakhādyaka,” which translates to “edible bite.” This text, in contrast to the theoretical nature of his earlier work, served as a more practical guide for astronomers and surveyors. It provided valuable insights into the calculation of various celestial phenomena, such as eclipses, planetary positions, and lunar and solar cycles.

Legacy and Impact

Brahmagupta’s contributions to mathematics and astronomy extended far beyond his time. His pioneering ideas and theories laid the foundation for the development of modern mathematics and the scientific understanding of celestial bodies. The concept of gravity as an attractive force, as described in the “Brāhmasphuṭasiddhānta,” was a remarkable precursor to Isaac Newton’s groundbreaking work in the 17th century.

Furthermore, Brahmagupta’s work on algebraic rules and number systems significantly influenced subsequent mathematicians in India and the Islamic world. His legacy can be seen in the algebraic notation and techniques that we use today.

Brahmagupta, a brilliant mathematician and astronomer of ancient India, left an indelible mark on the history of science. His theoretical treatise, the “Brāhmasphuṭasiddhānta,” and practical guide, the “Khaṇḍakhādyaka,” revolutionized our understanding of mathematics and astronomy. His description of gravity as an attractive force and his contributions to algebraic notation continue to inspire and shape the world of mathematics and science. Brahmagupta’s work serves as a testament to the enduring impact of knowledge and the brilliance of human innovation.

By Mala Chandrashekhar

Introducing Blogger Mala Chandrashekhar - a specialist academically trained in modern Western sciences, yet deeply enamored with India's timeless ethnic arts, crafts, and textiles. Her heart beats for the rich and glorious cultural and spiritual heritage of India, and she has dedicated her entire blog to spreading the immortal glories of ancient India worldwide. Through her simple yet impactful blog posts, Mala aims to reach every nook and corner of the globe, sharing India's beauty and wisdom with the world.

But Mala doesn't stop at just sharing her own thoughts and ideas. She welcomes constructive criticisms and suggestions to improve her blog and make it even more impactful. And if you share her passion for India's culture and heritage, she extends a warm invitation for high-quality guest blog posts.

Ready to dive into the world of India's ageless beauty? Follow Mala on LinkedIn and join her in spreading the magic of ancient India to the world.

LinkedIn Profile : https://in.linkedin.com/in/mala-chandrashekhar-04095917a

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Verbal Ability

• Interview Q

• Send your Feedback to [email protected]

Help Others, Please Share

Learn Latest Tutorials

Transact-SQL

Reinforcement Learning

R Programming

React Native

Python Design Patterns

Python Pillow

Python Turtle

Preparation

Interview Questions

Company Questions

Trending Technologies

Artificial Intelligence

Cloud Computing

Data Science

Machine Learning

B.Tech / MCA

Data Structures

Operating System

Computer Network

Compiler Design

Computer Organization

Discrete Mathematics

Ethical Hacking

Computer Graphics

Software Engineering

Web Technology

Cyber Security

C Programming

Control System

Data Mining

Data Warehouse

• study guides
• lesson plans
• homework help

Brahmagupta Biography

World of Mathematics on Brahmagupta

FOLLOW BOOKRAGS:

Brahmagupta’s Contributions in Mathematics

WARNING: unbalanced footnote start tag short code found.

If this warning is irrelevant, please disable the syntax validation feature in the dashboard under General settings > Footnote start and end short codes > Check for balanced shortcodes.

Unbalanced start tag short code found before:

“p+r)⁄2 × (q+s)⁄2), whereas, the exact area is given by  √(t − p)(t − q)(t − r)(t − s), where t = (p+q+r+s)⁄2. Also, Heron’s formula is a special case of the Brahmagupta formula, which can be obtained by setting one side equal to zero. 8. Brahmagupta Theorem Brahmagupta theo…”

1. Properties of Zero

According to him, zero is a number that is obtained, when a number is subtracted from itself. He also mentioned some properties of zero, where positive numbers are termed as fortunes and negative numbers are termed as debt.

• When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.
• 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 multiplied by zero is zero.
• The product or quotient of two fortunes is one fortune.
• The product or quotient of two debts is one fortune.
• The product or quotient of a debt and a fortune is a debt.
• The product or quotient of a fortune and a debt is a debt.

He also tried to make some conclusions on the division by zero. For this he said,

Positive or negative numbers when divided by zero is a fraction with zero as denominator. Zero divided by negative or positive numbers is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.”

2. Brahmagupta’s Method of Multiplication

He proposed a method of multiplication, “gomutrika”, in his book “Brahmasphutasiddhanta”. The title of this method was translated by Ifrah as, “Like the trajectory of cow’s urine”. In the 12th chapter of his book, he also tried to explain the rules of simplifying 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. Let us try to multiply 315 by 306 with the help of the gomutrika method.

Now multiply the 306 of the top row by the 3 in the top position of the left-hand column. Begin by 3 × 6=  18 , putting 8 below the 6 of the top row, carrying 1  in the usual way to get

Now multiply the 306 of the second row by the 1 in the left-hand column writing the number in the line below the 918 but moving one place to the right

Now multiply the 306 of the third row by the 5 in the left-hand column writing the number in the line below the 306 but moving one place to the right

Now add the three numbers 91800 + 3060 + 1530 = 96390 is the required result.

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

306       5

306       1

306       4

In the third variant of this method, just write each number once but otherwise follows the second method.

3. Intermediate Equations

Brahamgupta proposed some methods to solve equations of the type ax + by = c. According to Majumdar, Brahmgupta used continued fractions to solve such equations. He also tried to solve quadratic equations of the type ax² + c = y² and ax² – c = y². For example, for the equation 8x² + 1 = y² he obtained the solutions as (x, y)= ( 1 , 3 ) , ( 6 , 1 7 ) , ( 3 5 , 9 9 ) , ( 2 0 4 , 5 7 7 ) , ( 1 1 8 9 , 3 3 6 3 ) , . .He also solved 61x² + 1 = y²  having solution as x = 226153980, y = 1766319049 as its smallest solution. 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.”

4. Sum of Series

He gave the sum of, a series of cubes and a series of squares for the first n natural numbers as follows:

1² + 2² +…….+n² = (n)(n+1)(2n+1)⁄6

1³ + 2³ +…….+n³ = (n(n+1)⁄2)²

5. Pythagorean triplets

Brahmagupta in chapter 12, entitled “Calculation”, of his book, proposed a formula that was useful in generating Pythagorean triplets. 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.”

If d= mx ⁄(x+2), then a traveller who leaps vertically upwards, a distance d from the top of the mountain of height m and, then covers a horizontal distance of mx from the base of the mountain, in a straight line, to the city, travels the same distance, as the one who descends vertically down the mountain and then travels along the horizontal line to the city. Geometrically this means, if a right-angled triangle has a base of length a = mx and altitude of length b = m + d, then the length, c, of its hypotenuse is given by c = m (1+x) – d. And, elementary algebraic manipulation shows, that a 2  + b 2  = c 2  whenever d  has the value stated. 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.

6. Pell’s Equation

Brahmagupta studied this equation 1000 years before Pell’s birth. Pell’s equation is of form, n x ² + 1 = y², which can also be written as y² – nx² = 1, where ‘n’ is an integer and we have to solve it for (x, y) integer solutions. Brahmagupta also provided a lemma, in which he stated that if ( a , b ) and ( c, d) are integer solutions of ‘Pell type equations’ of the form                    na²+ k = b²  and  nc² + k’ = d² then, (bc + ad, bd + nac)  and  (bc – ad, bd – nac) are both integer solutions of the ‘Pell type equation’ nx² + kk’ = y². Brahmagupta used the method of composition to find solutions for Pell’s equations. He composed (a, b) and (a, b) to get (2ab, b² + na²) as a solution to Pell’s equation. After getting (2ab, b² + na²) as a solution of the equation nx² + k² = y², he divided the x and y coordinates by k² which gave x = 2ab⁄k² and y = b² + na²⁄k², a solution of Pell’s equation of the form nx² + 1 = y². He then claimed, that with the help of the composition method one can generate many solutions to Pell’s equation.

7. Brahmagupta’s Formula

Brahmagupta’s formula for the cyclic quadrilaterals is regarded as his most famous discovery in geometry. Given the sides of a cyclic quadrilateral, he provided an approximate and exact formula for the area of the cyclic quadrilateral. He mentioned,

 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.”

In the figure below, p, q, r, s are the sides of the cyclic quadrilateral. Its approximate area is given by ((p+r)⁄2 × (q+s)⁄2), whereas, the exact area is given by  √ (t − p)(t − q)(t − r)(t − s), where t = (p+q+r+s)⁄2. Also, Heron’s formula is a special case of the Brahmagupta formula, which can be obtained by setting one side equal to zero.

8. Brahmagupta Theorem

Brahmagupta theorem states that,

If a cyclic quadrilateral is orthodiagonal (i.e., has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.”

Geometrically, this theorem means that, in a cyclic quadrilateral ABCD, diagonals AC and BD are perpendicular to each other. The intersection of AC and BD is M.  Drop the perpendicular from M to the line BC, calling the intersection point E. Let F be the intersection of the line EM and the side AD. Then, according to the theorem, F is the midpoint of side AD. Brahmagupta further extended his theory and claimed that,

 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.”

The above statement means that in an isosceles trapezoid having sides of length p, q, r, s, the length of the diagonal is given by √pr+qs.

9. Triangles

A major portion of Brahmagupta’s work was dedicated to the study of geometry. One of his theorem about triangles states that,

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.”

This theorem gives the length of two segments in which the base of a triangle is divided by its altitude, and the lengths are, 1 / 2 (b ± ( c 2  − a 2) / b ) . He also discussed rational triangles. A rational triangle with the rational area and sides a, b, c, are of the form:

a = 1⁄2(u²⁄v + v), b = 1⁄2(u²⁄w + w), c = 1⁄2(u²⁄v – v + u²⁄w – w), for some rational numbers u, v, w.

10. Approximation of π

Brahmagupta also tried to approximate the value of π and in stanza 40 of his book he mentioned,

 The diameter and the square of the radius, each multiplied by 3 are the practical circumference and the area of a circle respectively. The accurate values are the square-roots from the squares of those two multiplied by ten.”

He used √10 ≈ 3.1622….. approximated to 3, as an accurate value of π with an error of less than 1%.

11. Mensuration and Construction

Brahmagupta illustrated the construction of several figures with arbitrary sides. He tried to construct figures such as isosceles triangles, scalene triangles, rectangles, isosceles trapezoids, isosceles trapezoids with three equal sides, and scalene cyclic quadrilateral, mainly, with the help of right triangles. He also gave the volume and surface area of some figures, after estimating the value of π. He found the volume of rectangular prisms, pyramids and frustum of a square pyramid. He further proposed the average depth of a series of pits.

12. Trigonometry

Brahmagupta, in chapter 2 of his book, provided a sine table. He wrote,

The sines: The Progenitors, twins, Ursa Major, the Vedas, the gods, fires, flavors, dice, the moon, the sky, the moon, arrows, sun…..”

He used the above objects to represent digits of place-value numerals. Progenitors represent 14 progenitors in Indian cosmology, twins means 2, Ursa Major represents the seven stars of Ursa Major or 7, Vedas refers to the 4 Vedas or 4, dice represents the number of sides of the traditional die or 6, and so on. He gave the sine table with 3270 as radius and calculated 3270 sin(π⁄48). For 1 ≤ n ≤ 24, he got values as 214, 427, 638, 846, 1051, 1251, 1446, 1635, 1817, 1991, 2156, 2312, 2459, 2594, 2719, 2832, 2933, 3021, 3096, 3159, 3207, 3242, 3263, and 3270.

13. Interpolation formula

Brahmagupta was the first who propose an interpolation formula using second-order difference. His Sanskrit verses on this formula were found in the Khandakadyaka work of Brahmagupta. Today, the Brahmagupta interpolation formula is known as Newton- Stirling interpolation formula. In his book, he termed the difference D r as the ‘gatakhanda’,  the difference D r+1 as the ‘bhogyakhanda’, ‘Vikala’ as the quantity in minutes by which the interval has been covered at the point of interpolation, which in modern notation denoted as a − x r . ‘Sphuta-bhogyakhanda’ is now known as   f r+1 − f r . A formula stated by him, for the computation of values of the sine table, having common interval (h) in the underlying base table as 900 minutes or 15 degrees, is given below.

When translated these verses means,

Multiply the ‘vikala’ by the half the difference of the ‘gatakhanda’ and the ‘bhogyakhanda’ and divide the product by 900. Add the result to half the sum of the ‘gatakhanda’ and the ‘bhogyakhanda’ if their half-sum is less than the ‘bhogyakhanda’, subtract if greater. The result in each case is ‘sphuta-bhogyakhanda’ the correct tabular difference.

In modern notation, the formula is denoted as

sphuta-bhogyakhanda =  ( D r + D r-1) ⁄2 ± t| D r –  D r-1 |⁄2, where ± is introduced according to   D r  < D r+1  or  D r  > D r+1  and f(a) is given by,

f(a) = f r + t × sphuta-bhogyakhanda, is known as Stirling’s interpolation formula for second-order differences.

14. Algebra

Brahmagupta gave the solution of general linear equations in chapter 18 of his book and wrote,

The difference between rupas, when 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.”

Algebraically, the above statement means that, for an equation of type bx+c = dx+e, the solution is given by x = e − c / b − d. He also gave two solutions for the quadratic equation ax² +bx = c, and wrote, 

 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.”

By this method, the solution is given by, x = ±(√(4ac+b²) – b)⁄2a.

 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. The result is the unknown.”

By this method, the solution is given by, x = ±(√(ac+b²⁄4) – b²⁄2)⁄a.

Related Posts

12 Everyday Life Examples of Cube

Aryabhata’s Contributions in Mathematics

22 Examples of Mathematics in Everyday Life

9 Real Life Examples Of Normal Distribution

Aristotle’s Contributions in Mathematics

8 Poisson Distribution Examples in Real Life

Add comment cancel reply.

• Ancient Science & Technology
• Myths and Legends

Ancient Instrument described in Vaimanika shastra

The science behind om mantra, ancient hindu temples stand on a straight line, astronomical instruments of bhaskaracharya, ghatika yantra – the ancient indian water clock, raireshwar temple – where shivaji took the oath of hindu swarajya, significance of 9 days of chaitra navratri, sanchi stupa – 3rd century ancient buddhist monument, lachit borphukan – the unsung hero who stopped mughals from conquering northeast india, chitradurga fort- history, architecture, temples, tourist attractions and visiting times, chamundeshwari temple- history, legend, significance and popular rituals, bhai dooj (day 5 of diwali)- significance, history, and everything you need to know, govardhan puja (day 4 of diwali)- significance, history, and everything you need to know, bhuthanatha temple- history, architecture, and popular attractions, aihole fort- history, legend, architecture and popular attractions, mysterious work on ajanta caves, tsunami might have destroyed harappan port town of dholavira, over 10,500 years old camping site discovered in ladakh, 1,000-year-old hindu temple excavated in bangladesh, the submerged temples of mahabalipuram, indian origins of zoroastrians or parsees, the zoroastrians or parsees – the forgotten children of india, dasharajnya – the battle of ten kings, similarities between noah’s ark and manu’s boat, mystery of sri yantra geoglyph in oregon dry lake bed, eternal flames of jwala ji temple, magnetic hill of ladakh, krishna’s butter ball – a balancing rock at mahabalipuram, mystery of red rain in india.

• Indus Valley Civilization

Bhaskaracharya – The great Astronomer and Mathmatician

Shrinathji Temple, Nathdwara – Lord Krishn’s Chosen Spot

Top 15 magnificent rock-cut caves in india, varahamihira – indian sage who predicted water discovery on mars 1500 years ago.

T he period between 500 and 1200 AD was the golden age of Indian Astronomy. During this golden period an Indian wizard was born who contributed greatly to the conception of Astronomy and Mathematics. He was none other than Bhaskaracharya.

Bhaskaracharya was the leading mathematician and Astronomer of the 12th century, who wrote the first work with full and systematic use of the decimal number system. He was born near Vijjadavida (Bijapur in modern Karnataka). Bhaskaracharya’s name was actually ‘Bhaskara’ only but the title ‘Acharya’ was added and conferred to mean “Bhaskara the Teacher”. He is also known as Bhaskaracharya II.

Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He became head of the astronomical observatory at Ujjain, the leading mathematical centre in India at that time. Outstanding mathematicians such as  Varahamihira and Brahmagupta had worked there and built up a strong school of mathematical astronomy.

There are six well known works of Bhaskaracharya. They are :- Lilavathi – Mathematics, Bijaganita – Algebra, Ganitadhyaya – mathematical astronomy, Goladhyaya – sphere, Karanakutuhala – Calculation of Astronomical Wonders, Vasanabhasya – Bhaskara’s own commentary on the Siddhanta Shiromani, and Vivarana which is a commentary on the Shishyadhividdhidatantra of Mathematician and Astronomer Lalla .

Bhaskara was known not only for his mathematical scholarship, but also for his poetic inclinations. He wrote Lilawati in an excellent lucid and poetic language. It has been translated in various languages throughout the world. It was written for his daughter, Lilavati. The Lilavati deals with arithmetic and geometry; it is said that the name is after his daughter Lilavati, who was according to her horoscope to remain unmarried.

In his mathematical works, particularly Lilavati and Bijaganita, he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation (x2 = 1 + py2) and in giving many particular solutions.

Bhaskara anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero. Bhaskara used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees.

Brahmagupta was Bhaskara’s role model. To Brahmagupta he pays homage at the beginning of his Siddhanta Siromani. Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately calculated the time that earth took to revolve around the Sun as 365.2588 days that is a difference of 3 minutes of modern acceptance of 365.2563 days.

Bhaskaracharya was the first to discover gravity , 500 years before Sir Isaac Newton. He is also known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. Bhaskara’s work on calculus predates Newton and Leibniz by over half a millennium.

Bhaskara has given a very simple method to determine the circumference of the Earth. According to this method, first find out the distance between two places, which are on the same longitude. Then find the correct latitudes of those two places and difference between the latitudes. Knowing the distance between two latitudes, the distance that corresponds to 360 degrees can be easily found, which the circumference of the Earth.

He also showed that when a planet is farthest from, or closest to, the Sun, the difference between a planet’s actual position and its position according to the equation of the centre(which predicts planets’ positions on the assumption that planets move uniformly around the Sun) vanishes. He therefore concluded that for some intermediate position the differential of the equation of the centre is equal to zero.

Some other achievements of Bhaskaracharya were:

• The Earth is not flat, has no support and has a power of attraction.
• The north and south poles of the Earth experience six months of day and six months of night.
• One day of Moon is equivalent to 15 earth-days and one night is also equivalent to 15 earth-days.
• Bhaskaracharya had accurately calculated apparent orbital periods of the Sun and orbital periods of Mercury, Venus, and Mars. There is slight difference between the orbital periods he calculated for Jupiter and Saturn and the corresponding modern values.
• Earth’s atmosphere extends to 96 kilometers and has seven parts.
• There is a vacuum beyond the Earth’s atmosphere.

Bhaskaracharya, or Bhaskara II (1114 – 1185) is regarded almost without question as the greatest mathematician of all time and his contribution to not just Indian, but world mathematics is undeniable. He was perhaps the last and the greatest astronomer that India ever produced.

 Source:   Free Press Journal & Veda Wikidot

• Bhaskaracharya
• Brahmagupta
• mathematicians
• Mathematics
• Surya Siddhant

More articles

Latest article

Editor picks, popular posts, holy man hasn’t eaten or drank for 70 years, popular category.

• Ancient Place 43
• Hinduism 33
• Archaeology 29
• Ancient Science & Technology 22
• Indus Valley Civilization 15

MysteryOfIndia is dedicated to the land of mysteries - India. We aim to showcase interesting information about India and its rich heritage. Connect with us on Facebook & Twitter (X) to share more inputs.

With Love for India

© MysteryOfIndia.com