In the forthcoming articles we highlight some of the major contributions of celebrated astronomers like ARYABHATA, BRAHMAGUPTA, BHASKARACHARYA, MADHAVA, NILAKANTHA SOMAYAJI, et. al. in the field of Astronomy and Mathematics. In this issue First we would like to share with readers as to how Western scientists were astonished at the predictions made by Indians in the field of Astronomy. The science of Astronomy had been taken to such great heights around the end of the 18th century that the astronomers of other traditions were really wonder – struck and puzzled by the accuracy of the predictions.

For instance, a fascinating review of the Indian knowledge system in Astronomy was done by JOHN PLAYFAIR (1748-1819) in a paper titled THE ASTRONOMY OF BRAHMINS published in the TRANSACTIONS OF THE ROYAL SOCIE FY OF EDINBURGH IN 1790. PLAYFAIR was a mathematician, physicist, geologist, astronomer and historian, who held the position of Professor of Natural Philosophy at the University of Edinburgh. He was really puzzled that the accuracy of the Indian predictions was always better than that made by the Ptolemaic system and that it often matched with those being made in Europe around his time (end of the 18th century, when European science was flourishing with post-Newtonian confidence). While speculating reasons for the extraordinary accuracy in their predictions, PLAYFAIR observes:

“…Some ‘ages ago’ there had arisen a NEWTON among the brahmin-s, to discover that universal principle which connects, not only the most distant regions of space, but the most remote periods of duration; and a LAGRANGE, to trace, through the immensity of both, its most subtle and complicated operations”.

This is one of the hypotheses made by PLAYFAIR and it is very interesting to notice that:

* PLAYFAIR acknowledges the fact that there were great observers in India while the entire Europe was barbarous or uninhabited (This is quite apparent from his own usage of the words “ages ago”).

Secondly, he compares the ‘poor’ brahmins of India to the stalwarts of Western science like NEWTON and LAGRANGE, whose findings have really made significant contributions to the progress of science. This comparison not only means that there were great mathematicians in India, but also is indicative of the fact that their analytical faculty and intellectual outputs in the field of astronomy and mathematics were comparable to those of NEWTON and LAGRANGE.

In fact the entire paper of JOHN PLAYFAIR is characterized by wonder. He repeatedly remarks on the “wonderful certainty and precision” of the “ingenious”, “extraordinary” and “extremely simple” rules that the Indians used. It is not difficult to list a host of other Western scholars who have joined PLAYFAIR and expressed their admiration but the point I would like to make is that many of us are not aware of our own contributions to science. More interestingly, even people who do not generally admire India’s contribution to science, have acknowledged that Indians were far more successful than the medieval Europeans. For instance DAVID PINGREE (2001) a renowned scholar says:

The way medieval Indian astronomers and mathematicians pursued science was demonstrably different and in many ways “far more” successful than the way in which medieval Europeans pursued Astronomy and Mathematics’.

**Â ARYABHATA AND HIS CONTRIBUTIONS :**

Aryabhata’s magnum opus, the Aryabhatiya 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.

Aryabhattas ideas about eclipses and the sun being the source of moonlight may not have caused much of an impression on European astronomers as by then they had come to know of these facts through the observations of Copernicus and Galileo. But considering that Aryabhata discovered these facts 1500 years ago, and 1000 years before Copernicus and Galileo makes him a pioneer in this area too. Aryabhata’s methods of astronomical calculations expounded in his Aryabhata Â¬ siddhanta were reliable for practical purposes of fixing the Panchanga (Hindu calendar). Thus in ancient India, eclipses were also forecast and their true nature was perceived at least by the astronomers.

The lack of a telescope hindered further advancement of ancient Indian astronomy, though it should be admitted that with their unaided observations with crude instruments, the astronomers in ancient India were able to arrive at near perfect measurement of astronomical movements and predict eclipses.

Indian astronomers also propounded the theory that the earth was a sphere. Aryabhata was the first one to have propounded this theory in the 5th century Another Indian astronomer, Brahmagupta estimated in the 7th century that the circumference of the earth was 5000 yojanas. A yojana is around 7.2 kms. Calculating on this basis we see that the estimate of 36,000 kms as the earth’s circumference comes quite close to the actual circumference known today.

Aryabhata was the first scientist to provide an approximate value for the mathematical constant Â Ï€(pi). Generally, we say n 22/ 7, but actually Aryabhata had more to say !

He gives the value correct to five decimal places. A circle of diameter 20,000 units has a circumference approximately equal to (100 + 4) x 8 + 62,000 = 62,832. This can be represented in the form of an equation:

Ï€ (circumference / diameter) = (62,832 / 20,000) = 3.1416. What is really remarkable in the work of Aryabhata is the use of the word aasanna, which means approximately. This contribution of Aryabhata was proved only about 8 centuries later !

*Â To be continued….*