Ancient Mathematician & Astrologer Aryabhata

Aryabhata born December 476 CE Ashmaka is old name of Patna (Bihar) India was the first in the line of great mathematician- astrologer from the classical age of  Indian Mathematician and astronomer . His works include the Aryabhata (499 CE, when he was 23 years old) and the Arya-SidinataThe works of Aryabhata dealt with mainly mathematics and astronomy. 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 , plan trigonometry, and spherical trigonometry . It also contains continued fractions , quadratics equations, sums-of-power series, and a table of sines.

The Arya- siddhanta, a lost work on astronomical computations, is known through the writings of Aryabhata’s contemporary, Varahamihira , and later mathematicians and commentators, including Brahmagupta and Bhaskara. This work appears to be based on the older surya siddhanta  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.

Aryabhatiya Main article: Aryabhatiya  Direct details of Aryabhata’s work are known only from the Aryabhatiya. The name “Aryabhatiya” is due to later commentators. Aryabhata himself may not have given it a name. His disciple Bhaskar  calls it Ashmakatantra . It is also occasionally referred to as Arya-shatas-aShTa (literally, Aryabhata’s 108), because there are 108 verses in the text. It is written in the very terse style typical of sutra (formula) literature, in which each line is an aid to memory for a complex system. Thus, the explication of meaning is due to commentators. The text consists of the 108 verses and 13 introductory verses, and is divided into four pādas or chapters:

1. Gitikapada: (13 verses): large units of time—kalpa, manvantra, and yuga—which present a cosmology different from earlier texts such as Lagadha’s Vedanga Jyotisha  (c. 1st century BCE). There is also a table of sins (Jya) , given in a single verse. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years.
2. Ganitapada (33 verses): covering menstruation  (kṣetra vyāvahāra), arithmetic and geometric progressions, gnomon / shadows (shanku-chhAyA), simple, quadratic ,simultaneous , and indeterminate equations
3. Kalakriyapada (25 verses): different units of time and a method for determining the positions of planets for a given day, calculations concerning the intercalary month (adhikamAsa), kShaya-tithis, and a seven-day week with names for the days of week.
4. Golapada (50 verses): Geometric/ trigonometric  aspects of the celestial sphere, , features of the elliptical equator , celestial equator , node, shape of the earth, cause of day and night, rising of zodiacal signs  on horizon, etc. In addition, some versions cite a few colophons  added at the end, extolling the virtues of the work, etc.

The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, c. 600 CE) and by Nilkantha Somayaji  in his Aryabhatiya Bhasya, (1465 CE).

To be continue…….1