Aryabhata quotes
The development of Indian trigonometry, based on sine as against chord of the Greeks, a necessity for astronomical calculations with his own concise notation which expresses the full sine table in just one couplet for easy remembrance. One of the two methods suggested by him for the sine table is based on the property that the second order sine differences were proportional to sines themselves.
Aryabhata
His work, called Aryabhatiya, is composed of three parts, in only the first of which use is made of a special notation of numbers. It is an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, ...., 100 etc. The other mathematical parts of Aryabhatiya consists of rules without examples. Another alphabetic system prevailed in Southern India, the numbers 1-19 being designated by consonants, etc.
Aryabhata
Use of better planetary parameters, the innovations in astronomical methods, and the concise style of exposition of Aryabhatiya makes it an excellent text book on Astronomy. As opposed to the geostationary theory, Aryahabata held the view that the earth rotates on its axis. His estimate of the period of the sidereal rotation of earth was 23 hours 56 min, and 4.1 s is close to the actual value.
Aryabhata
His fame rests mainly on his Aryabhatiya, but from the writings of Varahamihira (Sixth century AD), Bhaskara I, and Brahmagupta (seventh century) it is clear that earlier he composed the Aryabhata Siddhantha (voluminous) is not extant. It is also called Ardharatrika Siddhanta, because in it the civil days were reckoned from one midnight to the next; 34 verses on astronomical instruments from this have been quoted by Ramakrishna Aradya.
Aryabhata
He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes.
Aryabhata
... it is extremely likely that Aryabhata knew the sign for zero and the numerals of the place value system. This supposition is based on the following two facts: first, the invention of his alphabetical counting system would have been impossible without zero or the place-value system; secondly, he carries out calculations on square and cubic roots which are impossible if the numbers in question are not written according to the place-value system and zero.
Aryabhata
Aryabhata is acknowledged as one of the astute astronomers of early India. His school of astronomy is well known and widespread all over India, especially in the South...Of late there is a tendency to spell his name as "Aryabhatta”. While Aryabhata himself mentions Kali 3600 to be the date of his composing the work, some say that Kali 3600 is the date of his birth. A view has been broached that Aryabhata hailed from Kerala.
Aryabhata
He was a celebrated astronomer and mathematician of the classical period of the Gupta Dynasty...He played an important role in shaping scientific astronomy in India. He is designated as Arayabhata I to differentiate him from Arya Bhata II who flourished much later (ca. AD 950-1100) and who wrote the Mahasiddhanta.
Aryabhata
In Ganita, he names the first 10 decimal places and gives algorithms for obtaining square and cubic roots, utilizing the decimal number system. Then he treats geometric measurements - employing 62,832/20,000 (= 3.1416) for π-and develops properties of similar right-angled triangles and of two intersecting circles.
Aryabhata
