Information about Aryabhatta.

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1. History of the great Indian Mathematician. aryabhatta

2. Birth Aryabhata mentions in the  Aryabhatiya  that it was composed 3,600 years into the  Kali yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476.Aryabhata provides no information about his place of birth. The only information comes from  Bhaskara 1, who describes Aryabhata as  āśmakīya , "one belonging to the asmaka  country." During the Buddha's time, a branch of the Aśmaka people settled in the region between the  Narmada  and  Godavari  rivers in central India; Aryabhata is believed to have been born there.

3. It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time .  Both Hindu and Buddhist tradition, as well as  Bhaskara 1  (CE 629), identify Kusumapura as  Pataliputra, modern  Patna verse mentions that Aryabhata was the head of an institution ( kulapa ) at Kusumapura, and, because the university of  Nalanda  was in Pataliputra at the time and had an astronomical observatory, it is speculated that Aryabhata might have been the head of the Nalanda university as well .  Aryabhata is also reputed to have set up an observatory at the Sun temple in  Taregana, Bihar . education

4. Aryabhata is the author of several treatises on  mathematics and   astronomy, some of which are lost.His major work,  Aryabhatiya , a compendium of mathematics and astronomy, was extensively referred to in the Indian mathematical literature and has survived to modern times. The mathematical part of the  Aryabhatiya  covers  arithmetic,   algebra,   plane trigonometry and   spehrical trigonometry. It also contains  continued fractions,   quadraticiquations, sums-of-power series, and a  table of sinesThe   Arya-siddhanta , a lost work on astronomical computations, is known through the writings of Aryabhata's contemporary,  Varahamihira, and later mathematicians and commentators, including  Bramhagupta  and  Bhaskara 1. This work appears to be based on the older  Surya Sidhhanta and uses the midnight-day reckoning, as opposed to sunrise in  Aryabhatiya . It also contained a description of several astronomical instruments: the  gnomon  ( shanku-yantra ), a shadow instrument ( chhAyA-yantra ), possibly angle-measuring devices, semicircular and circular ( dhanur-yantra  /  chakra- yantra ), a cylindrical stick  yasti-yantra , an umbrella-shaped device called the  chhatra-yantra , and  water clocks  of at least two types, bow-shaped and cylindrical. A third text, which may have survived in the  Arabic  translation, is  Al ntf  or  Al- nanf . It claims that it is a translation by Aryabhata, but the Sanskrit name of this work is not known.Probably dating from the 9th century, it is mentioned by the  Persian scholar and chronicler of India,  Abu Rayhan al Biruni Works

5. Aryabhata's system of astronomy was called the  audAyaka system  (days are reckoned from  uday ,  dawn at  lanka ,  equator). Some of his later writings on astronomy, which apparently proposed a second model ( ardha-rAtrikA , midnight), are lost, but can be partly reconstructed from the discussion in Brahmagupta's   khanDakhAdyaka . In some texts he seems to ascribe the apparent motions of the heavens to the earth's rotation. astronomy

6. Aryabhata appears to have believed that the earth rotates about its axis. This is made clear in the statement, referring to  Lanka,  which describes the movement of the stars as a relative motion caused by the rotation of the earth: "Like a man in a boat moving forward sees the stationary objects as moving backward, just so are the stationary stars seen by the people in lankA (i.e. on the equator) as moving exactly towards the West ."But the next verse describes the motion of the stars and planets as real movements: “The cause of their rising and setting is due to the fact the circle of the asterisms together with the planets driven by the protector wind, constantly moves westwards at Lanka.” Motions of the solar system

7. Aryabhata stated that the  Moon  and planets shine by reflected sunlight. Instead of the prevailing cosmogony, where eclipses were caused by pseudo-planetary nodes Rahu and Ketu , he explains eclipses in terms of shadows cast by and falling on earth. Thus, the lunar eclipse occurs when the moon enters into the earth-shadow (verse gola.37), and discusses at length the size and extent of this earth-shadow (verses gola.38-48), and then the computation, and the size of the eclipsed part during eclipses. Subsequent Indian astronomers improved on these calculations, but his methods provided the core. This computational paradigm was so accurate that the 18th century scientist Guillaume le Gentil , during a visit to Pondicherry, found the Indian computations of the duration of the  Lunar Eclipse  of 1765-08-30 to be short by 41 seconds, whereas his charts (Tobias Mayer, 1752) were long by 68 seconds . Aryabhata's computation of Earth's circumference was 24,835 miles, which was only 0.2 percent smaller than the actual value of 24,902 miles. This approximation might have improved on the computation by the Greek mathematician    Eratosthenes (c . 200 B.C.E.), whose exact computation is not known in modern units. eclipses

8. Considered in modern English units of time, Aryabhata calculated the sidereal rotation (the rotation of the earth referenced the fixed stars) as 23 hours 56 minutes and 4.1 seconds; the modern value is 23:56:4.091. Similarly, his value for the length of the sidereal year at 365 days 6 hours 12 minutes 30 seconds is an error of 3 minutes 20 seconds over the length of a year. The notion of sidereal time was known in most other astronomical systems of the time, but this computation was likely the most accurate in the period. Sidereal periods

9. Āryabhata claims that the Earth turns on its own axis and some elements of his planetary epicyclic models rotate at the same speed as the motion of the planet around the Sun. This has suggested to some interpreters that Āryabhata's calculations were based on an underlying heliocentric model in which the planets orbit the Sun .  A detailed rebuttal to this heliocentric interpretation is in a review which describes B. L. van der Waerden's book as "show[ ing ] a complete misunderstanding of Indian planetary theory [that] is flatly contradicted by every word of Āryabhata's description ,"  although some concede that Āryabhata's system stems from an earlier heliocentric model of which he was unaware .   It has even been claimed that he considered the planet's paths to be elliptical, although no primary evidence for this has been cited. Though Aristarchus of Samos (third century B.C.E.) and sometimes Heraclides of Pontus (fourth century B.C.E.) are usually credited with knowing the heliocentric theory, the version of Greek astronomy known in ancient India,  Paulisa Siddhanta  (possibly by a Paul of Alexandria) makes no reference to a Heliocentric theory. Heliocentrism

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11. http://en.wikipedia.org/wiki/Aryabhata http://www.newworldencyclopedia.org/entry/Aryabhata https://www.google.com/search?q=aryabhatta sources

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