Brahmagupta the Indian Mathematician – Facts about India

If you are a mathematician, an astronomy student, scientist or someone who loves leaning about facts about India then here’s something that you would like. Brahmagupta was an ancient Indian mathematician and astronomer who is credited with discovering the properties of zero.

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Let’s look at the life and discoveries of Brahmagupta

Brahmagupta an ancient Indian mathematician and visionary was born in the year 598 AD in the city of Bhinmal , which is presently in North West Rajasthan. He was a scholar of great name and fame at his time and taught at a university dedicated for mathematics, Sanskrit and scientific research in Ujjain. The university was patronized by Gujarat dynasty. Being the head of the observatory in the university of Ujjain he wrote four mathematical and astronomical related books Cadamekela in 624, the Brahmasphutasiddhanta in 628, the Khandakhadyaka in 665, and the Durkeamynarda in 672.

It is assumed that the works of Brahmagupta originally evolved through Greek Babylonian scriptures and literatures. His ideas were such that they soon began to travel to other countries like China and Bhagdad.

During this time Abbasid caliph al-Ma’mun had an embassy in India and it is believed that Brahmagupta Brahmasidhhanta was brought to the middle east city of Bagdaad and then later translated into Arabic form as Sind- Hind. Al-Biruni a renowned Arabic historian gives detailed account of this cultural transaction in his book Tariq al-Hind, from India to the Muslim world. The Muslim or Islamic calendar which is based on the lunar eclipse and positions of moon in the sky gives the most evident example of Vedic Islamic cultural alchemy.

The work of Brahmagupta not only inspired Arabic world but also surpassed the boundaries of middle Asia now called China. It is well known that Chinese scholars like Huan Tsing used to travel frequently to Buddhist land of India and many served as historians and ambassadors in the courts of Indian kings like HarshVardhana. In many of their cultural surveyed writings we find the mentions of great Indian mathematicians like Aryabhatta and Brahmagupta.

Aryabhatta, the Indian mathematician

Brahmagupta was the first to give the general solution for linear Diophantine equation ax + by= c, where a, b, and c are numerical integers. Brahmagupta used many example a of Diophantus in explaining the above linear equations, a clear similarity is also visible in the nature of algebra put forward by Brahmagupta and Greek scholars. These evidences show a clear cut socio cultural influence between Indian Brahmagupta and Greek Diophantus.

In the modern times the work of Brahmaguota has evolved from Stone Age to techno age. The concepts of gravity and the spherical nature of the earth were much polished by later scientist like Galileo and Newton who not only were limited to the gravity part but also configured and concluded the basic acceleration due to the force of gravity and found that the earth rotates on its axis and revolves around the sun which was in fact contrary to the idea of Brahmagupta who believed that the earth is a stationary heavenly body.

His simple formulae about the cyclic quadrilateral in a circle have become more complex and easier with the help of computers who bargain the millions of calculations in a wink of an eye.

The concept of “pulverizer” which was nothing but an algorithm put forward by Brahmagupta to break numbers into fractions of smaller proportions has evolved into dynamics of Physics integrations calculus dy/dx.

His assumptions and theories regarding the planetary positions and movements in time have not only been verified but also a travel to lunar soil has been undertaken.

His numeric ideas of zero, decimal and sine logs have been successfully utilized in various aspects of the present era be it calculation of currency, astronomy, constructions of designs or writing the basic algorithm of computer language which is “0, 1”.

Brahmagupta and his work in the field of mathematics science and astronomy have traveled space and time. It is literally hard to believe that a scholar more than 1500 years back could imagine theories and concepts which will govern our modern science and technological research work and that to in the absence of credible microscope governed by electricity and digital computers. Brahmagupta was a visionary who was not only intelligent but possessed some thing which was unique when it comes to the discussion of sixth sense of man in paranormal science. What we couldn’t see from our advanced telescopes and super computers he visualized it with naked eyes.
Significance of Brahamagupta discoveries in modern world.

Now if someone questions about the significance of Brahamgupta’s work it will be like questioning the existence of man itself. The contemporary era is marked by the exhaustive development of science and technology which in turn could only be possible by the hard labor of our present and ancient scientists and mathematicians.
Brahamgupta is one of the oldest and most praised after mathematician and holds the place equivalent to Newton in the legend of scientific and mathematical innovators. His work holds its importance not only in the pre-Newtonian times but also post Newtonian era. There are however various fields in which Brahmagupta’s work play crucial role some of them are discussed below.

Architecture:- The modern buildings use exclusive designs like domes and portions of circles example semicircular, hemicircular, quadracircular or the entire circle as a whole sometimes at the base of the structure or at the top of the sky scrapers while designing these structures architects use the formulae promulgated by Brahmagupta.

then exact area will be  given that p,q,r,s are length of the sides of rectangle within the circle  for proper proportions these calculations are extremely necessary.

Indian and Islamic calendars:– Brahamagupta is still playing an important role in the existing field of astronomy he calculated the positions of heavenly bodies ,he also concluded their rising and setting time frames and as to why the shape of the moon varies with the passing time not only this he also derived the true longitudes between different planets and between sun and moon ,the explanation of solar and lunar eclipses was also an effort by Brahamagupta in his book Brahmasphutasiddhanta (chapter 7) . Al-Biruni ,the famous Arabic scholar , translated Brahmasphutasiddhanta into Arabic as Sindhind .We are all aware of the fact that Indian and Islamic calendars are based on the positions of sun and moon and it was due to sheer genius of Brahamagupta ,which framed the basic foundation of the Indian and Islamic calendars.

Space and Science:- In the field of space and science Bhramagupta’s law of gravitations, sine tables and the concept of trigonometry forms the very foundation of the launch space vehicles. For proper launching of a space craft the correct angle is of paramount importance for the proper trajectory of the vehicle along with much emphasis on the thousands of decimal calculations with due consideration of gravity by the super computers. But it is to be remembered that the original data fed into these computers by human hands can be traced back as late as Bramagupta’s book Brahmasphutasiddhanta. The concept of gravity was first propounded by Bhramagupta and later renovated by Newton himself.

Water supply or sewage system:– For an efficient and modern town architecture its sewage system should not only be unique but should also support the population present and growing ones. Water supply to the entire city is also very necessary for a civilization to grow by leaps and bounds. The entire concept of water drainage and consumption is based upon thousands of spider webs of pipes lying underground across the city. Bramagupta’s concept of measuring volume length breadth and height of circular and cylindrical objects still plays a crucial role when planning a town.

These were just 4 examples of what Brahmaputa’s concept are put into while implementing our contemporary lifestyle although there are thousands of other applications which are construed directly or indirectly through Brahmagupta’s concept of mathematics, but people fail to realize that and continue reaping the harvest of the seeds sown by Brahmagupta. Many scientist and mathematicians have evolved during the cycle of earth’s technological development and have made a number of significant discoveries for the betterment of mankind, but Brahmagupta and his book Brahmasphutasiddhanta still forms the very foundation of approximately every scientific development in the field of engineering, mathematics, astronomy and architecture and will continue to hold their importance in years to come.

BRAHAMAGUPTA a general view of his enormous work

Life is a sum of complex numbers and man is hypnotized by the ever growing volumes, density, unknown factors, addition, subtraction, series, algorithms and geometry of his destiny and always wished a way to predict his future. Well the answer lies in many hidden pits of numbers and its mentor the great visionary from India named Brahamagupta famous for his work in the field of mathematics and the art of fore telling, the science known as astronomy.

A brief review of his genuine intelligent work will prove why he is called the mentor of numbers and astronomy:

1) Algebra:- In the field of mathematics, this art is construed for finding the missing links or the unknown factor X as generally taught to us in our schools. The key significance is Algebra always concludes the factor X required to distribute salary percentage or ratio in which the proper distribution has to be made. Brahamagupta gave three formulas

1) X=e-c / b-d
2) X=√4ac+b2 –b/2a
3) X=√ac+b2 /4-b/2

The basic difference between these simplified formulates and the original ones is that he placed numbers side by side for addition and dots for subtraction for division he placed divisor below dividend and represented multiplication by abbreviations.

2) Arithmetic: – This is in-fact the most commonly used ancient art of calculation. Here Brahamagupta in chapter 12 of his famous book Brahmasphutasiddhanta promulgates five types of fraction combinations

3) Series: -Our maths teachers often exclaimed “2″ raised to the power of n plus the natural number series”. The squares and cubes, its quiet confusing for a novice but this visionary has that answer which many of our teachers forget to tell us. He gives the sum of the squares of the first n natural numbers as n(n+1)(2n+1)/6 and the sum of the cubes of the first n natural numbers as (n(n+1)/2).

4) Other accomplishments:– Among other accomplishments of Brahamagupta comes the discovery of Zero and its calculations with different negative and positive integers, in chapter 12 Brahamagupta discusses the details about Diophantine analysis , Pythagorean triples and Pell’s equation for breaking numbers into several pieces and theorems relating to generalization of identity

5) Geometry:– Brahamagupta was equally a past master in the field of shapes sizes and volumes he developed formulae and concepts to measure area and exact area of cyclic quadrilateral

His other discoveries include the value of pi and methods of measuring length, breath volume and depth.

Although he made so many mathematical discoveries his sine tables based on the trigonometrical longitudes of planets aid a lot in modern gigantic calculations and calculations in the field of astronomy. What Galileo and Newton felt at later stages about earth’s shape and gravity Brahamgupta had discovered hundreds of years ago.

Acknowledging such vast collection of mathematical discoveries of Bhramagupta it will be an honor to call him mentor of words and that of medieval scientists of the Newtonian era from west.

BRAHAMAGUPTA INVENTED ZERO “0”

So you thought you knew everything well the answer may pop up “approximately” just because you are “educated” and are well armed with all the scientific knowledge of the western world doesn’t not mean you know everything in fact you know “0”. Most people will be quiet offended by this remark but solemnly do you really know zero. I am sure most of you know more than zero and less than zero but not the story of zero itself.

In this ever dynamic world who cares a damn about this sweet little zero, but imagine if this is taken out of our lives all the scientific developments will come to a chaotic end and your four to eight figure salary will be a single digit trauma, NASA will have to cancel trips to mars and moon, our modern mathematics will be equally shaken and will find new abrupt faces to explain its complex theorems ,in short the entire world will be a bear’s garden in the absence of this single numeral called ‘Zero’ and written as ‘0’.

By now people must have understood the impact of zero in our lives but still they are zero as most of them don’t even know who discovered zero, unfortunately for many Indians and western big shots the answer will be scanned among great scientist like Einstein, Galileo or perhaps Newton. These literates are too inspired by the awe of the western world and have forgotten that science and mathematics did existed even in the most ancient cultures and countries be it in Egypt, China or India.

Zero was not the brainchild of western world but the product of an Indian mathematician called Brahamagupta in 598 AD. Brahamagupta was born in Gujarat in the city of Bhinmal which is presently in North West Rajasthan. Brahamagupta was the head of the department of mathematics and Astronomy at the university set up by another great Vedic Indian mathematician Aryabhata at the city of Ujjain which was at that time a great center for learning Science literature Sanskrit and the art of prediction called astronomy.

In chapter 18 of his famous book called Brahmasphutasiddhanta (Corrected Treatise of Brahma) Brahamagupta describes about Zero as one of the numerals which stood for meaning nothing. He also elaborates as to how integers positive and negative consequence when played with zero.

For example

ADDITION WITH ZERO
if a positive integer value is added to a similar negative value the result is zero,the sum of a negative integer and a zero is negative , sum of a positive integer and a zero is positive and the addition of two zero’s is zero.

SUBTRACTION WITH ZERO
.A negative integer subtracted from zero is negative, a positive integer subtracted from zero is positive and a zero subtracted from zero is zero.

MULTIPLICATION WITH ZERO
A negative integer, positive integer and a zero with Zero will always be Zero.

SQUARE AND SQUAREROOT OF ZERO
The square of a zero and squawroot of a zero is always zero.

DIVISION WITH ZERO
A zero divided by a zero is zero and a negative or positive integer divided by zero is zero.

Only at this point of division Brahamagupta makes crucial mistake as we all know that an integer divided by zero is not zero but in-finite. Brahamagupta is criticized by many contemporary and ancient scholars and mathematicians for this ardent mistake but what they fail to realize is the very foundation Brahamagupta provided to the platform of science and mathematics by using Zero as numerals for the first time and that too successfully. There is another side of the coin which still needs to be reviewed, it state that an integer when divided by 0 is 0 which most of the scientists believe is wrong but the synonym of 0 is “shunaya or Shunya” which is fortunately also the same for “infinite”. However it is a matter of debate and still in hypothesis weather Brahamagupta knew about the concept of infinite/undefined or not but scanning his astronomical geniuses he possessed it can be safely assumed that he was well acquainted with the theorem.

Zero is not just a word or a numeral it is a symbol of the pride of East and the fact that the eastern culture’s research and development in the field of science and mathematics is the very foundation on which the medieval western discoveries were made and yet more future ones still remain to be made through forgotten zeroes of the east..

The gravitational pull of Brahamagupta and Newton

Brahamagupta the greatest of all Indian mathematicians was born in Gujarat in the city of Bhinmal which is presently in North West Rajasthan. His work regarding the application of numerals, discovery of zero ,discovery of pi ,”sutras” or formulae in the field of arithmetic, algebra, series, Pells Equation, Diophantine analysis, area of cyclic quadrilaterals in geometry, trigonometry, planetary true longitudes ,astronomy and GRAVITATION make him the oldest geniuses of eastern scientific world.

Sir Isaac Newton born 4th January 1643 in Woolsthorpe, Lincolnshire in England was the greatest English mathematician of his generation. He laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.

Brahamagupta wrote his famous book Brahmasphutasiddhanta in which he describes in detail the content of his work Brahmagupta’s Karanakhandakhadyaka is a handbook on astronomical calculations. Brahamagupta believed that the earth was stationary but he firmly believed that it was round. His beliefs further include the positioning of sun and moon he cleverly argues about the distance of sun to be greater than moon from the earth based on the solar and lunar eclipse, one of the most crucial discovery by Brahamagupta was that he was the first to give his view about gravity and believed that it was the nature of the earth to hold and attract things towards itself.
Sir Isaac Newton wrote many famous books one of the most recognized and acclaimed one was Principia mathmatica ,Newton describes the law of motion and the gravitational pull of the earth in this book. His other works include Method of Fluxions (1671) Of Natures Obvious Laws & Processes in Vegetation (1671–75) unpublished work on alchemy De Motu Corporum in Gyrum (1684) ,Optics (1704) etc. It is said that Newton also had a belief in the art of occult.

It was said that when Newton was hit by an apple from the tree he came the realization of gravitational force of the earth. While Brahamagupta’s more accurate philosophical arguments like “all heavy things are attracted towards the center of the earth. The earth on all its sides is the same; all people on 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.” Seem to be a more realistic reason for a theory.

Sir Isaac Newton was awarded the credit of the discovery of the force of gravity when the same discovery was made approximately 1000 years before by Brahamhagupta in India ,it is far by no doubt that both were great scientists and renowned autocrats of their times but giving the entire credit for a discovery which was already made earlier is something like giving credit to a bulb factory worker ,who just finished making a bulb, for the invention of bulb altogether indeed the new bulb will have a better filament and shine than the one discovered by Tomas Elva Edison .If we unfortunately do so, we will be too rude to all the sweat that Edison must have drained while discovering an electric bulb .Similarly the world is still being rude to the greatest Indian genius Brahamagupta when it comes to the discovery of gravitational pull.

When it comes to the work on optics Brahamagupta was equally aware of the astronomical heavenly bodies like Newton and has given much logical explanations in terms of sine tables and true longitudes as Newton’s explanation of the acceleration due to gravity 9.8 m/s2 .It is possible that the concept of speed ,acceleration ,velocity etc was not known nor required at the time of Brahamagupta hence the theorems in these pre texts were not initiated in these directions .

Sir Newton believed in occult and predicted the end of the world by 2050 based on what facts is still in the shades of doubts Brahamagupta developed a science of numbers called astrology which was based on the positions of planets and stars through it the future of the individual could be predicted.

The only difference between Newton and Brahamagupta was that in the origin and era assuming it to be true that the work of Brahamagupta was discovered by the western world at a later stage but some credit must necessarily be given to the original inventor of the concept of gravitation along with the contemporary Newtonian one after all true science is based on the facts and conceptual realities rather than just plain simple origin .The decision should be left on the people and the world to be decided, which gravitational pull is attracting them more Newton or Brahamagupta’s.