History of Indian Mathematics

[stranger]

But I would not be surprised if someone comes up with a twisted interpretation of some vedic hymns and proclaims that we indeed were the world leaders in NMR.

I want to see Devapriya beating Bruker and Varian using his novel technology called Vedic transform NMR!

When Vasco da Gama reached India, he immediately launched a campaign of terror to avenge Cabral's men who had been killed by Muslim rioters in Calicut. Vasco da Gama's first act was to capture a passenger ship carrying Muslim families home to Calicut from a pilgrimage to Mecca. After looting the ship, Vasco da Gama set fire to it, deliberately burning to death hundreds of women and children.
He next sent an ultimatum to the Zamorin of Calicut, ordering him to kill all the Muslims in his city, or face retaliation. When the Zamorin offered to negotiate a compromise, Vasco da Gama began capturing Hindu fishermen from Calicut, and chopping off their hands, feet, and heads. He then bombarded the city, aiming to kill as many civilians as possible.
By his aggressive actions, Vasco da Gama demonstrated that Portuguese ships, with their superior cannon, were able to dominate their competitors, the traditional Arab merchant ships of the Indian Ocean. Muslim merchant ships were frightened away from Calicut, disrupting the city's trade.
Although Vasco da Gama returned to Portugal in 1503, other Portuguese commanders in India imitated his tactics of seaborne terror, with devastating results for the economy of Calicut. In 1513 the Zamorin of Calicut negotiated a trade agreement with the Portuguese.
Portugal established an empire in India, and Vasco da Gama became viceroy of the Indian colonies. He was enormously rich when he died in Cochin, India, on Dec. 24, 1524.

Not more than 2000 people came in a Ship and looted India.

If these guys had gun-powder and knew how to make use of explosives why did not they do any effort to get rid of these looters???

What were they doing with gun-powder???

Sending them to Sivakasi for deepaavali fire-crackers???

[SRS]

Attempts have been made to discredit Aryabhatiya in this thread. For the record, Aryabhatiya was not "wrong." Here are some of his discoveries, according to Wikepedia:

His book, "?ryabhat?ya", presented astronomical and mathematical theories in which the Earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun (in other words, it was heliocentric).He believes that the Moon and planets shine by reflected sunlight and he believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon. His value for the length of the year at 365 days 6 hours 12 minutes 30 seconds is remarkably close to the true value which is about 365 days 6 hours. This book is divided into four chapters: (i) the astronomical constants and the sine table (ii) mathematics required for computations (iii) division of time and rules for computing the longitudes of planets using eccentrics and epicycles (iv) the armillary sphere, rules relating to problems of trigonometry and the computation of eclipses. In this book, the day was reckoned from one sunrise to the next, whereas in his "?ryabhata-siddh?nta" he took the day from one midnight to another. There was also difference in some astronomical parameters.
He was the first to explain how the Lunar Eclipse and the Solar Eclipse happened.
Aryabhata also gave close approximation for Pi. In the Aryabhatiya, he wrote: "Add four to one hundred, multiply by eight and then add sixty-two thousand. The result is approximately the circumference of a circle of diameter twenty thousand. By this rule the relation of the circumference to diameter is given." In other words, ? ? 62832/20000 = 3.1416, correct to four rounded-off decimal places.
Aryabhata was the first astronomer to make an attempt at measuring the Earth's circumference since Erastosthenes (circa 200 BC). Aryabhata accurately calculated the Earth's circumference as 24,835 miles, which was only 0.2% smaller than the actual value of 24,902 miles. This approximation remained the most accurate for over a thousand years.
He also propounded the Heliocentric theory of gravitation, thus predating Copernicus by almost one thousand years.
8th century Arabic translation of Aryabhata's Magnum Opus, the ?ryabhat?ya was translated into Latin in the 13th century. Through this translation, European mathematicians got to know methods for calculating the areas of triangles, volumes of spheres as well as square and cube root. Earlier Arabic translations of the ?ryabhat?ya were available in the Middle East by the 8th century, before the Crusades took place, so it's also likely that Aryabhata's work had an influence on European astronomy.
Aryabhata's methods of astronomical calculations have been in continuous use for practical purposes of fixing the Pancanga (Hindu calendar).
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Mathematics

One of the books of Aryabhatiya is on mathematics. Aryabhata describes the kuttaka algorithm to solve indeterminate equations. In recent times, this algorithm has also been called the Aryabhata algorithm.
He also created a novel alphabetic code to represent numbers that is now called the Aryabhata cipher.
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Overview

Accurately computed pi
Explained solar eclipses
Expounded a heliocentric model of the solar system and accurately computed the length of earth's revolution around the sun.
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[SRS]

Not only did Aryabhatta influence Indian mathematics, but he also had an impact on the development of Western mathematics (and astronomy as well). Unfortunately, some of our Dravidian friends will try to deny that, but even the Westerners acknowledge this basic fact.

[gaddeswarup]

Not only did Aryabhatta influence Indian mathematics, but he also had an impact on the development of Western mathematics (and astronomy as well). Unfortunately, some of our Dravidian friends will try to deny that, but even the Westerners acknowledge this basic fact.

As far as I know, most Indians as well as foreigners who know of some of Aryabhatta's work admire it. The problem comes when there are attempts to push some of the defects under carpet ( there are mistakes in the works of western mathematicians too). There is an artcle in EPW (September, 2003) entitled "Axiomitization and Computational Positivism" by Roddam Narasimha, FRS. Narasimha's theory is that the Indian astromers were not partcularly interested in theories but predictions. They seem to have been remarkably successful in this ; the accuracies of some of the predictions of Aryabhatta and others have not been surpassed until the 18th century. He calls this computational positivism. When I wrote to him saying that Aryabhatta and Bhaskara could have easily verified their farmulae by a few crude experiments, there has been no response.
The last bit is from an earlier thread :
http://forumhub.mayyam.com/hub/viewt...r=asc&start=15
where the topic was discussed at some length. I think that Sri Aravindhan has added more information in this thread. The trouble is that if we want to bridges, we cannot use all of Aryabhatta's work uncritically. Regards,
swarup

[SRS]

Not only did Aryabhatta influence Indian mathematics, but he also had an impact on the development of Western mathematics (and astronomy as well). Unfortunately, some of our Dravidian friends will try to deny that, but even the Westerners acknowledge this basic fact.

As far as I know, most Indians as well as foreigners who know of some of Aryabhatta's work admire it. The problem comes when there are attempts to push some of the defects under carpet ( there are mistakes in the works of western mathematicians too). There is an artcle in EPW (September, 2003) entitled "Axiomitization and Computational Positivism" by Roddam Narasimha, FRS. Narasimha's theory is that the Indian astromers were not partcularly interested in theories but predictions. They seem to have been remarkably successful in this ; the accuracies of some of the predictions of Aryabhatta and others have not been surpassed until the 18th century. He calls this computational positivism. When I wrote to him saying that Aryabhatta and Bhaskara could have easily verified their farmulae by a few crude experiments, there has been no response.
The last bit is from an earlier thread :
http://forumhub.mayyam.com/hub/viewt...r=asc&start=15
where the topic was discussed at some length. I think that Sri Aravindhan has added more information in this thread. The trouble is that if we want to bridges, we cannot use all of Aryabhatta's work uncritically. Regards,
swarup

No one is saying Arayahatta was 100% correct on all accounts. In fact, no one cares that Arayabhatta may have been wrong on a few trivial points, except our Dravidian friends here. In typical fashion, they choose to dwell on these few points. Hiding what under the carpet? The list of Aryabhatta's achievements is long and respected (except of course by our Dravidian friends). Because he did not "experimentally" verify every astronomical calculation is not a reason to dismiss his work. As I have said before, mathematical discovery must come before the scientific application. This is why the ancient Indians were such excellent astronomers: l they were also excellent mathematicians. This is what sees in Ramanujan, in fact. That the Indian mind was already comprehending advanced mathematics. Ramanujan the Brahmin! Who will deny that he was influenced by Vedas?

[1&only]

How does a Zero becomes a Hero? When it is given to world by Arabs then a zero turns to hero.

How does a Hero becomes a zero? When it insists on vedic supremacy.

You need it explained? Don't hesitate to ask me!