Aryabhata the Elder,astronomer mathematician of the ancient world
476 CE
Adapted From Wikipedia, the free encyclopedia
Aryabhata (??????) Aryabhata) (476 – 550)(2765BCE- 2691 BCE) is the first of the great mathematician-astronomers of the classical age of India. He lived in Kusumapura, which his commentator Bhaskara I (629 AD)( ? BCE ) identifies with Pataliputra (modern Patna).There is little doubt that till the advent of the 20th century he was one of the greatest astronomers of all time in human history. There is considerable uncertainty as to the antiquity of Aryabhata. There is evidence in his own works that he gives an accurate dating as to when he lived. Quoting from the book by Lakshmikantham and Leela (Origin of Mathematics)
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"Aryabhata is the first famous mathematician and astronomer of Ancient India. In his book Aryabhatteeyam, Aryabhata clearly provides his birth data. In the 10th stanza, he says that when 60 x 6 = 360 years elapsed in this Kali Yuga, he was 23 years old. The stanza of the sloka starts with “Shastyabdanam Shadbhiryada vyateetastra yascha yuga padah.”
“Shastyabdanam Shadbhi” means 60
x 6 = 360. While printing the
manuscript, the word “Shadbhi”
was altered to “Shasti”, which
implies 60 x 60 = 3600 years
after Kali Era. As a result of
this intentional arbitrary
change, Aryabhata’s birth time
was fixed as 476 A.D Since in
every genuine manuscript, we
find the word “Shadbhi” and not
the altered “Shasti”, it is
clear that Aryabhata was 23
years old in 360 Kali Era or
2742 B.C. This implies that
Aryabhata was born in 337 Kali
Era or 2765 B.C. and therefore
could not have lived around 500
A.D., as manufactured by the
Indologists to fit their
invented framework. The implications are profound , if indeed this is the case. The zero is by then in widespread use and if he uses Classical Sanskrit then he antedates Panini Here is another version of the verse which makes a big difference How It is Linked with the Dates of Indian astronomers? The ancient Indian astronomers perhaps purposely linked the determination of their dates of birth, composition of their works, calculation of number of years elapsed, etc., based on two eras Kali and Saka. Therefore, without the significance of these two eras, the dates cannot be determined specifically. Shastabdhanam shastiryadha vyatitastrashyam yugapadha| Trayadhika vimsatirabdhastdheha mama janmanoatita|| "When sixty times sixty years and three quarter yugas (of the current yuga) had elapsed, twenty three years had then passed since by birth" (K. S. Shukla). "Now when sixty times sixty years and three quarter Yugas also have passed, twenty increased by three years have elapsed since my birth" (P. C. Sengupta). "I was born at the end of Kali 3600; I write this work when I am 23 years old i.e, at the end of Kali 3623" " (T. S. Kuppanna Sastry11). Here, though only Yuga is mentioned, Kaliyuga is implied and its starting of 3102 BCE is taken for reckoning purpose. Thus, the date of Aryabhata is determined as follows: The year of birth = 3600 – 3102 = 488 / 499 – 23 = 476 CE. This has been accepted by most of the scholars and generally considered as accepted date. Had the commencement year 3102 BCE is a myth or not astronomical one, the year of Aryabhata cannot be historical date or could be detrmined like this using 3102 BCE. Bhaskara I in his commentary to Aryabhatiya mentions as follows (Ch.I.verse.9): Kalpadherabdhnirodhadhayam abdharashiritiritaha: khagnyadhriramarkarasavasurandhrenadhavaha: te cangkkairapi 1986123730 | "Since the beginning of the current Kalpa, the number of years elapsed is this: zero, three, seven, three, twelve, six, eight, nine, one (proceeding from right to left) years. The same (years) in figures are 1986123730". Kalpadherabdhanirodhat gatakalaha: khagnyadhriramarkarasavasurandhrenadhavaha: te ca 1986123730
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ASTRONOMIC
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Àryabhata
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Surya
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Years in Cycle |
4,320,000 |
4,320,000 |
|
Rotations |
1,582,237,500 |
1,582,237,828 |
|
Days |
1,577,917,500 |
1,577,917,828 |
|
Lunar Orbits |
57,753,336 |
57,753,336 |
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Kay notes 57,753,339 lunar orbits rather than 57,753,336 per Clarke. |
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Synodic Months |
53,433,336 |
53,433,336 |
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Mercury |
17,937,920 |
17,937,060 |
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Venus |
7,022,388 |
7,022,376 |
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Mars |
2,296,824 |
2,296,832 |
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Jupiter |
364,224 |
364,220 |
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Saturn |
146,564 |
146,568 |
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Table 1. Comparison of The Àryabhatiya of Àryabhata and Astronomic values. |
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Astronomy Constants |
AD 2000.0 |
AD 500 |
1604 BC |
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Rotations per solar orbit |
366.25636031 |
366.2563589 |
366.25635656 |
|
Days per solar orbit |
365.25636031 |
365.2563589 |
365.25635656 |
|
Days per lunar orbit |
27.32166120 |
27.3216638 |
27.32166801 |
|
Rotations per lunar orbit |
27.39646289 |
27.39646514 |
27.39646936 |
Aryabhatiya
His book, "Aryabhatiya", is a tour de force in which he not only represented 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) but laid the foundation for a mathematical infrastructure to solve future problems in the field of Astronomy.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 "Aryabhata-siddhanta" he took the day from one midnight to another. There was also difference in some astronomical parameters.
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, p ˜ 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 a feat that Erastosthenes of the Library of Alexandria (circa 200 BC) emulated much later. 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 3 thousand years. Of course, Christopher Columbus was not cognizant of the accurate value for the circumference , since the correct number would have indicated a much longer voyage than he had anticipated
He also propounded the Heliocentric theory of the universe, thus predating Copernicus by almost one thousand years, and if we accept the earlier date by as much as 4000 years.
The 8th century Arabic translation of Aryabhata's Magnum Opus, the Aryabhatiya was translated into Latin in the 13th century, before the time of Copernicus. Through this translation, European mathematicians may have learned methods for calculating square and cube roots, and it is also possible 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 Panchanga (Hindu calendar).
Recently his name has been in the news because RSA Conference 2006 chose their theme to be ancient Vedic Mathematics and Aryabhata. Indocrypt 2005 had a invited talk on vedic mathmatics. As more and more conferences with information security professionals focus on vedic Mathematics, it is believed that vedic Mathematics will have profound effect on cryptographic systems.
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.
Aryabhata, in his work Aryabhata-Siddhanta, first defined the sine as the modern relationship between half an angle and half a chord, while also defining the cosine, versine, and inverse sine. His works also contained the earliest tables of sine values and versine (1 - cosine) values, in 3.75° intervals from 0° to 90°, to an accuracy of 3 decimal places. He used the words jya for sine, kojya for cosine, ukramajya for versine, and otkram jya for inverse sine. The words jya and kojya eventually became sine and cosine respectively after a mistranslation (see Etymology above).
Overview
- Accurately computed pi
- Explained and computed solar eclipses and lunar eclipses
- Expounded a heliocentric model of the solar system
- Accurately computed the length of earth's revolution around the sun.
External links
- Aryabhata-Life and contributions, second edition, by Hooda D.S., and J. N. Kapur, New Age International Publishers,2001,ISBN: 81-224-1305-6
- John J. O'Connor and Edmund F. Robertson. Aryabhata at the MacTutor archive.
- An essay on Aryabhata with references
- RSA Conference 2006
