ARYABHATT (476 CE) MASTER ASTRONOMER AND MATHEMATICIAN
Born in 476 CE in Kusumpur ( Bihar ), Aryabhatt's intellectual brilliance remapped the boundaries of mathematics and astronomy. In 499 CE, at the age of 23, he wrote a text on astronomy and an unparallel treatise on mathematics called "Aryabhatiyam." He formulated the process of calculating the motion of planets and the time of eclipses. Aryabhatt was the first to proclaim that the earth is round, it rotates on its axis, orbits the sun and is suspended in space - 1000 years before Copernicus published his heliocentric theory. He is also acknowledged for calculating p (Pi) to four decimal places: 3.1416 and the sine table in trigonometry. Centuries later, in 825 CE, the Arab mathematician, Mohammed Ibna Musa credited the value of Pi to the Indians, "This value has been given by the Hindus." And above all, his most spectacular contribution was the concept of zero without which modern computer technology would have been non-existent. Aryabhatt was a colossus in the field of mathematics.
5 comments:
Did You Know?
By D.P. Agrawal
Question: Did you know who was Aryabhatt and what was his date?
Answer: Aryabhatt was a great mathematician and astronomer of ancient India.
Date of Aryabhata:
Kâlakriya 20: When sixty times sixty years and three quarters of the yugas (of this yuga) had elapsed, twenty three years had then passed since my birth
(In Aryabhata's system of measuring time, 3600 of the Kali era corresponds to mean noon at Ujjain, on March 21, 499 CE (Sunday). So Aryabhata was born in 476 CE.) All other authors known by name are later to Aryabhata I, and mention his theories while refuting them or correcting them. The dates for Varahamihira have been verified also by independent techniques.)
Question: Did you know that Aryabhatt had propounded the view that earth was round.
Answer: He compared the Earth to a Kadamba flower as explained in the following quaotes.
Gola 6: The globe of the Earth stands (supportless) in space at the centre of the celestial sphere....The Earth is circular on all sides.
Gola 7: Just as the bulb of a Kadamba flower is surrounded by blossoms on all sides, so also is the globe of the Earth surrounded by all creatures whether living on land or in water.
(The very term Gola means sphere or round. Vatesvara, explicitly mentions a popular belief about the Earth being supported on the back of a turtle, and points out its deficiencies, "What does the turtle rest upon, etc". But no other reputed astronomer seems to have taken such possibilities seriously enough even to contest them.)
Question: Did you know that Aryabhatt propounded in the 5th Century AD that the Earth rotates and not the celestial sphere?
Quotes:
Gola 9: Just as a man in a moving boat sees the stationary objects on the land moving in the opposite direction, so also the stationary stars are seen by a person at Lanka as moving exactly towards the West. (Lanka is an imaginary point on the equator at which the Meridian of Ujjayini intersects the Equator. Ujjayini is the modern-day Ujjain. Thus, Aryabhata's Lanka is below the current-day Lanka. The Meridian of Ujjayini is was later copied by instituting the Meridian of Greenwich. )
Gola 10: It only appears to an observer at Lanka as if the celestial sphere and the asterisms and planets move to the West...to cause their rising and setting.
(This view is rejected by later authors, like Varahamihira, Brahmagupta etc. on the grounds that if it is the Earth that rotates, then clothes on a line will fly, and the falcon, which rises high in the sky will not be able to find its way back. Others say, the tops of trees will be destroyed, the ocean will invade the land etc.)
Question: Did you know that Aryabhatt had worked out the duration of the day at the poles?
Quotes:
Gola 16: The gods living in the north at the Meru mountain (north pole) see one half of the Bhagola (celestial sphere with its centre at the centre of the earth) as revolving from left to right (i.e., clockwise); the demons living in the south at Badvâmukha (south pole) see the other half rotating from right to left (i.e., anti-clockwise).
Gola 17: The gods (at the north pole) see the sun after sunrise for half a solar year; so do the demons (at the south pole). Those living on the moon see the sun for half a lunar month; the humans here see it for half a civil day.
(Wooden and iron models were used to demonstrate the spheres. Bhagola is the celestial sphere centred at the centre of the earth, while Khagola is the sphere centred on the observer. The principal circles of the Bhagola are the celestial equator, the ecliptic etc., while the principal circles of the Khagola are the horizon, the meridian, the prime vertical etc. For the related concepts of spherical astronomy, consult any text on spherical astronomy.)
Question: Did you know that Aryabhatt had given an accurate value of pi (p)?
Quotes:
Rational approximation to pi
Ganita 10: 104 multiplied by 8 and added to 62000 is the approximate circumference of a circle whose diameter is 20,000.
(That is, pi = 62832/20000 = 3.1416. This value of pi was widely used in the Arabic world. In Europe, this value is cited by Simon Stevin in his book on navigation, The Haven Finding Art, as the value known to the "ancients" which he states (correctly) as far superior to any value known to the Greeks. Unlike what current-day historians would have us believe, Egypt does not mean Greece to Simon Stevin. In any case Aryabhata's value is better than that of Ptolemy (3.141666), who lived in Alexandria, in Egypt. Simon Stevin, a Dutch mathematician, astronomer and navigator, introduced the decimal system in Europe, c. 1580, and gives a table of sine values like Aryabhata, correcting the earlier table given by Nunes. Better values of pi were subsequently obtained in Europe using the "Gregory" series for the arctangent, and faster convergent methods, all of which are found in works of the Aryabhata school, which were imported into Europe in the 16th and 17th c. (Gregory does not claim originality.) The Sanskrit term for approximate is asanna, a term also used in the sulba sutra. The Chinese had a better value of pi than Aryabhata, just as al Kashi had a more accurate value of pi than Nîlkantha. However, none of those values had the potential of the calculus, and neither Chinese nor al Kashi had equally accurate sine values. (Ptolemy does not even mention sines.) The Chinese value may well have been a fluke, while al-Kashi's value was based on extremely laborious computation. Neither had the future potential or the sweep that Aryabhata's approximation techniques had. These techniques were later developed by his school into the "Taylor" series for arctangent, the sine and the cosine.)
(Information on Aryabhatt and his work was kindly given by C.K. Raju, Professor of Math and Computer Science, Bhopal, India)
KAVi
there u ar kavi, thanks to add more info on this topic, with looots of LOVE R.Visva
Varahamihira
Aryabhatta is said to have discovered the diurnal motion of the earth' which he thought to be spherical. I leave the explanation of these scientific matters to those who are making scientific investigations of Hindu Astronomy. But one thing is certain that it was about this time that the old Krttika series of asterisms was discarded and the new series commencing from the 1st point of Asvini was adopted. The first point of ASvini recedes one degree or by one day in 73 years and it has receded twenty days now giving a total of twenty into seventy-three (20 X 73) that is, 1460 years. The point was on the equinoctial circle on the first day of Vaisakha and now it is on the 10th of Ohaitra. So the point was seen there 1460 years ago, that is, 1921-1460 that is 461 A.D. This is only an approximate calculation. If accurate calculation is made it will fall within the active period of Aryabhata's life.
Aryabhatta had many students and his next successor Lalla was one of his pupils and some say Varahamihira, too, was his pupil.
Aryabhatta had another celebrated astronomer as his contemporary. This was Varahamihira. In his Vrhajja- taka in the 26th chapter, he says that he was son of Adityadasa, that he was an Avantaka, that he received his knowledge from his father and that he obtained a book from the Sun-God at Kampillaka or Kapitthaka. Bhattotpala tells us that he was a Migadha dvija. Some say that he was a Magadvija, i.e., one of the Magii long settled in India. From all this the late Pandit Sudhakara Dvivedi in his Ganakatarangiui infers that it is not impossible that Varaha was a Magadha Brahmin. He might have gone to Ujjain for livelihood He studied with his father at his own house in Magadha and also studied the works of Aryabhatta there, he travelled to make himself known, he worshipped Sun-God at Kampillaka (Kalpi) and obtained a book from him. I acquired a manuscript of his son's work Prthuyasah-Sastra at Samkhu the northernmost part of the Nepal valley, the opening verse of which says that the son Varahamihira asked his father some questions while he was residing at the beautiful city of Kanyakubja on the Ganges.
Varaha might have retired to Kanyakubja in his old age to be on the Ganges and there imparted his knowledge to his son Prthuyasah. Amaraja, the commentator of Khandanakhandakhadya says that Varahamihira died in the Saka year 509 that is 587 A.D. Some people think that Varaha wrote his Panca-Siddhantika in 505 A.D. that is Saka 4:27. But this is impossible if we are to believe Amaraja. Varaha would then be only 18. Therefore Dr Thibaut after carefully considering all the facts of the case thinks that 427 Saka was the date when Lalla revised the Romaka-Siddhanta and that the Panca-SiddhSnta was composed about 550 A.D. So Varahamihira was a later contemporary and perhaps a student of Aryabhata.
The Ganakatarangiui has given a list of Varaha’s works and thinks that the Vrhat-Saipbita is his last work. It is an Eucyclopoedic work. It treats not only of Astronomy and Astrology but of such subjects as gardening, agriculture, sculpture, strilak^ana, purusalakgana and so on. This great work is the Pafica-Sidhantta in which he gives a summary of all the Sidhantas current in his time. They are five in number Paulisa, Romaka. VaSi^tha, Paitamaha and Sur.yyasiddhaata. Varaha says that of these five PmiliSa and Roraaka have been explained by Latadeva.
The Siddhanta made by PauliSa is accurate. Near to it stands the Siddhanta proclaimed by Romaka, more accurate is the Savitra (Saura) and the two remaining are far from the truth.
Kern says that the third Skandha of Jyotisa "'namely, its Jataka section has been borrowed from the Yavanas or Greeks. This is a fact. The Yavana-Jataka of Yavan&caryya is still regarded as an authoritative work on the subject and there are other works like Miuaraja Jataka also taken from the Yavanas. I found in Nepal a manuscript of a Yavana-Jataka written in the character of the tenth century oa palm-leaf which contains the following statement at the end.
sakthish....
Final comments on Aryabhatta
ARYABHATTA being the earliest author known to have treated of Algebra among the Hindus, and being likely to be, if not the inventor, the improver, of that analysis, by whom too it was pushed nearly to the whole degree of excellence which it is found to have attained among them; it becomes in an especial manner interesting to investigate further.
ARYABHATTA appears to have had more correct notions of the true explanation of celestial phenomena of his predecessors.
Considering the proficiency of ARYABHATTA in astronomical science, and adverting to the fact of his having written upon Algebra, as well as to the circumstance of his being named by numerous writers as the founder of a sect, or author of a system in astronomy, and being quoted at the head of algebraists, when the commentators of extant treatises have occasion to mention early and original writers on this branch of science, it is not necessary to seek further for a mathematician qualified to have been the great improver of the analytic art, and likely to have been the person, by whom it was carried to the pitch to which it is found to have attained among the Hindus.
sakthish.....
Post a Comment