Brahm Gupta

Wow Facts

Brahma Gupta ~ Great Indian Mathematician and Famous Scientists Brahmagupta

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.

Brahmagupta
Lived 597 – 668 AD
Brahmagupta is unique. He is the only scientist we have to thank for discovering the properties of precisely zero…

Brahmagupta was an Ancient Indian astronomer and mathematician who lived from 597 AD to 668 AD. He was born in the city of Bhinmal in Northwest India. His father, whose name was Jisnugupta, was an astrologer.

Although Brahmagupta thought of himself as an astronomer who did some mathematics, he is now mainly remembered for his contributions to mathematics.

Many of his important discoveries were written as poetry rather than as mathematical equations! Nevertheless, truth is truth, regardless of how it may be written.

Quick Guide to Brahmagupta
Brahmagupta:

was the director of the astronomical observatory of Ujjain, the center of Ancient Indian mathematical astronomy.
wrote four books about astronomy and mathematics, the most famous of which is Brahma-sphuta-siddhanta ( Brahma’s Correct System of Astronomy, or The Opening of the Universe.)
said solving mathematical problems was something he did for pleasure.
was the first person in history to define the properties of the number zero. Identifying zero as a number whose properties needed to be defined was vital for the future of mathematics and science.
defined zero as the number you get when you subtract a number from itself.
said that zero divided by any other number is zero.
said dividing zero by zero produces zero. (Although, this seems reasonable, Brahmagupta actually got this one wrong. Mathematicians have now shown that zero divided by zero is undefined – it has no meaning. There really is no answer to zero divided by zero.)
was the first person to discover the formula for solving quadratic equations.
wrote that pi, the ratio of a circle’s circumference to its diameter, could usually be taken to be 3, but if accuracy were needed, then the square-root of 10 (this equals 3.162…) should be used. This is about 0.66 percent higher than the true value of pi.
indicated that Earth is nearer the moon than the sun
incorrectly said that Earth did not spin and that Earth does not orbit the sun. This, however, may have been for reasons of self-preservation. Opposing the Brahmins’ religious myths of the time would have been dangerous.
produced a formula to find the area of any four-sided shape whose corners touch the inside of a circle. This actually simplifies to Heron’s formula for triangles.
said the length of a year is 365 days 6 hours 12 minutes 9 seconds.
calculated that Earth is a sphere of circumference around 36,000 km (22,500 miles).

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

adding two negative numbers together always results in a negative number.
subtracting a negative number from a positive number is the same as adding the two numbers.
multiplying two negative numbers together is the same as multiplying two positive numbers.
dividing a positive number by a negative, or a negative number by a positive results in a negative number.

Why is Zero Important?
Although it may seem obvious to us now that zero is a number, and obvious that we can produce it by subtracting a number from itself, and that dividing zero by a non-zero number gives an answer of zero, these results are not actually obvious.

The brilliant mathematicians of Ancient Greece, so far ahead of their time in many ways, had not been able to make this breakthrough. Neither had anyone else, until Brahmagupta came along!

It was a huge conceptual leap to see that zero is a number in its own right. Once this leap had been made, mathematics and science could make progress that would otherwise have been impossible.

Update September 14, 2017
Scientists at the University of Oxford have established that an Indian manuscript dated 200-400 AD is the first documented use of zero, as shown in the video below. Zero was invented before Brahmagupta’s era !

Detailed explanations:

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 one such genius Astronomer – Mathematician

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:

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.

This was a revolution as most people dismissed the possibility of a negative number thereby proving that quadratic equations (of the type

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.

Brahmagupta Formula

Area=√(S−p)(S−q)(S−r)(S−s)Where S=(p+q+r+s) 2 (see below image )

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

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.

Summary
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’.

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