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Life and the works of Aryabhatta (Aryabhata)

Pataliputra
was the birth-place of another very great man, namely, Aryabhata, the father of scientific astronomy and mathematics of the Hindus. He was born in 476 A D. and wrote his Kalakriyapada here at the age of 23 that is, 499 A.D.
Aryabhatta's Birthplace

There seem to have been a conflict of Eras at the time when Aryabhata flourished. There was the Malava Era in Western Malwa, the Gupta Km known in the Gupta Empire, the Saka Era, the Kalacuri Era and so on all local and tribal eras.
Time of Aryabhatta

Aryabhatta is the first writer on astronomy to whom the Hindus do not allow the honour of a divine inspiration. Writers on mathematical science distinctly state that he was the earliest uninspired and a merely human writer on astronomy. This is a notice which sufficiently proves his being an historical character.
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The chief doctrines which Aryabhatta professed were that he He affirmed the diurnal revolution of the earth on its axis; an assertion which is fully borne out by a quotation from one of his works, in a commentary on the "Brahmasphut'a-Siddhanta" of Brahmagupta by Prithudakaswami: "The Earth making a revolution produces a daily rising and setting of the stars and planets". Aryabhatta is said to have discovered the diurnal motion of the earth' which he thought to be spherical.
Aryabhatta's diurnal motion

Aryabhatta had another celebrated astronomer known as Varahamihira as his contemporary. Varahamihira

Aryabhatta also ascribed to the epicycles, by which the motion of a planet is represented, a form varying from the circle and nearly elliptic.
The chief doctrines of Aryabhatta

Aryabhata wrote his Kala-kriya (calculation of time) here at the age of 23 that is, 499 A.D.
Aryabhatta and Astronomy

ARYABHATTA was author of the Arykshiasata (800 couplets) and Dasagi-tica (ten stanzas), known by the numerous quotations of BRAHMEGUPTA, BHAT'TATPALA, and others, who cite both under these respective titles. Works of Aryabhatta

ARYABHATTA’S text specifies the earth's diameter, 1050 yojanas; and the orbit or circumference of the earth's wind [spiritus vector] 3393 yojanas; which, as the scholiast rightly argues, is no discrepancy. Aryabhatta’s calculation of the earth’s diameter

UNDER the Abbasside Khalifs ALMANSU'R and ALMAMUN, in the middle of the eighth and beginning of the ninth centuries of the Christian era, the Arabs became conversant with the
Indian astronomy.
In the history of mathematical science, it has long been a question to whom the invention of Algebraic analysis is due? Among what people, in what region, was it devised? By whom was it cultivated and promoted? Or by whose labours was it reduced to form and system?

And finally from what quarter did the diffusion of its knowledge proceed? No doubt indeed entertained of the source from which it was received immediately by modern Europe; though the channel has been a matter of question. We are well assured, that the Arabs were our instructors in this study. But the Arabs themselves only play to the discovery of Algebra.

They were not in general inventors but scholars, during the period of their success of the sciences: and the germ at least of the Algebraic analysis is to be found among the Greeks in an age not precisely determined, but more than probably anterior to the earliest dawn of civilization among the Arabs: and this science in a more advanced state subsisted among the Hindus prior to the earliest disclosure of it by the Arabians to modern Europe.
Brahmi numerals in India in the 1st century AD
The points, in which the Hindu Algebra appears particularly distinguished from the Greek, are, besides a better and more comprehensive algorithm. Difference between Indian and Greek Mathematics

Algebra