Page 18 - April 2021
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         flourished at that time. Nalanda, founded in the 5th
century, was a revered Buddhist monastery (Mahavihara) and a world-renown university in the ancient kingdom of Magadha.
At its peak, it attracted schol-
ars and travellers from beyond
the subcontinent, such as from
Tibet, China, Korea and Cen-
tral Asia. Nalanda’s Buddhist monks were hungry for scien-
tific knowledge and took a keen interest in the works of Greek
and Mesopotamian scholars
who had made advances in as- tronomy, mathematics, physics
and related subjects. The intellectual churn at Nalanda made it one of the most sought after centres of learning in this part of the world.
ARYABHATA’S WORKS
Aryabhata wrote several books and trea- tises on mathematics and astronomy, some of which, however, have been lost forever. We know of those lost works through their mention in the works of later day scholars who would have been inspired by Aryabhata’s works.
However, Aryabhatiya, which has survived to the modern times, is the most well-known. Besides surviving as a book itself, this compendium of mathematics and astronomy has been referred to in Indian mathematical lit- erature throughout history.
The title Aryabhatiya may not have been given by its author himself; it was thus named by later day scholars. It has also been referred to as Ashmakatantra (Treatise by the Ashmaka) or Aryas- hatasashta (or Aryabhata’s 108), as it comprises 108 verses.
The text contains 108 verses and 13 introductory verses. It is divided into four chapters, such as:
1. Gitikapada, dealing with large units of time such as kalpa, manvantra and yuga.
2. Ganitapada, dealing with mensura- tion, arithmetic and geometric progres- sions
3. Kalakriyapada, dealing with different units of time and determining the posi-
Aryabhata, India’s first indigenous satellite launched on April 19, 1975
The Aryabhatiya was a complex text that could be understood only with the help of commentaries or bhashyas.
tions of planets
4. Golapada, dealing with geometric and trigonometric aspects of the celes- tial sphere
The Aryabhatiya was a complex text that could be understood only with the help of commentaries or bhashyas, and these commentaries continued to be written for centuries.
Aryabhata Siddhanta was another of his lost works that is mentioned fre- quently by later day scholars and com- mentators. What makes it important is the fact that this book propounded midnight, and not the sunrise, as the starting hour of each day.
LEGEND UNPARALLELED
So little is known about Aryabhata, yet he continues to stand tall among astronomers and mathematicians even 15 centuries after his time. What makes him such an unparalleled legend?
It his work in the field of astronomy and mathematics, unprecedented those many years ago, that has made him a scholar par excellence even in the 21st
century.
Modern estimates suggest
that Aryabhata calculated the earth’s circumference as 39,968 km, extremely close to the modern calculation of 40,074 km. It is incredible considering that he did not have any mod- ern scientific aid for help.
He calculated an accurate table of sines, considered the first sine table constructed in the history of mathematics. It is not a table in the modern sense, comprising values in rows and columns, but it is a computa- tion of the half-chords of cer-
tain set of arcs of a circle. It served as a standard table in ancient India and later scholars worked upon it and improved it further. It eventually resulted in the discovery of the power series expansions of the sine and cosine functions by Mad- hava of Sangamagrama (c. 1350 - 1425 CE), the founder of the Kerala school of astronomy and mathematics.
A hypothesis states that Aryabhata’s table may have been inspired by earli- er Greek works but there is no extant Greek work to prove the point.
As is evident in the first chapter of Aryabhatiya, Aryabhata propounded that the earth rotated about its axis daily and the apparent movement of the stars was due to the relative motion caused by the earth’s rotation and not due to the rotation of the sky, which was widely believed for many centuries thereafter.
He also stated that sun was the only source of light in the universe; not just other planets but even stars reflected the light of the sun.
Aryabhata also worked on the ap- proximation of pi and accurately calcu- lated it to three decimal places as 3.141. Though he did not use zero in his math- ematical verses and calculations, its use was implicit in his place-value system.
Aryabhata’s work was of great influ- ence in the Indian astronomical tradi- tion and influenced several neighbour- ing cultures through translations. The Arabic translation during the Islamic Golden Age (c. 820 CE) was particularly influential.
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