Friday, July 23, 2010

Aryabhata (476–550 CE)

astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. Known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name, he flourished in Kusumapura—near Patalipurta (Patna), then the capital of the Gupta dynasty—where he composed at least two works, Aryabhatiya (c. 499) and the now lost Aryabhatasiddhanta. Aryabhatasiddhanta circulated mainly in the northwest of India and, through the Sāsānian dynasty (224–651) of Iran, had a profound influence on the development of Islamic astronomy. Its contents are preserved to some extent in the works of Varahamihira (flourished c. 550), Bhaskara I (flourished c. 629), Brahmagupta (598–c. 665), and others. It is one of the earliest astronomical works to assign the start of each day to midnight.
Aryabhatiya was particularly popular in South India, where numerous mathematicians over the ensuing millennium wrote commentaries. Written in verse couplets, this work deals with mathematics and astronomy. Following an introduction that contains astronomical tables and Aryabhata’s system of phonemic number notation, the work is characteristically divided into three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola (“Sphere”).
In Ganita Aryabhata 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. Utilizing the Pythagorean theorem, he obtained one of the two methods for constructing his table of sines. He also realized that second-order sine difference is proportional to sine. Mathematical series, quadratic equations, compound interest (involving a quadratic equation), proportions (ratios), and the solution of various linear equations are among the arithmetic and algebraic topics included. Aryabhata’s general solution for linear indeterminate equations, which Bhaskara I called kuttakara (“pulverizer”), consisted of breaking the problem down into new problems with successively smaller coefficients—essentially the Euclidean algorithm and related to the method of continued fractions.
With Kala-kriya Aryabhata turned to astronomy—in particular, treating planetary motion along the ecliptic. The topics include definitions of various units of time, eccentric and epicyclic models of planetary motion (see Hipparchus for earlier Greek models), planetary longitude corrections for different terrestrial locations, and a theory of “lords of the hours and days” (an astrological concept used for determining propitious times for action).
Aryabhatiya ends with spherical astronomy in Gola, where he applied plane trigonometry to spherical geometry by projecting points and lines on the surface of a sphere onto appropriate planes. Topics include prediction of solar and lunar eclipses and an explicit statement that the apparent westward motion of the stars is due to the spherical Earth’s rotation about its axis. Aryabhata also correctly ascribed the luminosity of the Moon and planets to reflected sunlight.
The Indian government named its first satellite Aryabhata (launched 1975) in his honour.

Mathematicians born in India

Apastamba
Aryabhata I
Aryabhata II
Baudhayana
Bhaskara I
Bhaskara II
Bose
Brahmadeva
Brahmagupta
De Morgan
Govindasvami
Harish-Chandra
Hemchandra
Jagannatha
Jyesthadeva
Kamalakara
Katyayana
Lalla
Madhava
Mahavira
Mahendra Suri
Manava
Narayana
Nilakantha
Panini
Paramesvara
Patodi
Pillai
Prthudakasvami
Rajagopal
Ramanujam
Ramanujan
Sankara
 

Sommerville
Sridhara
Sripati
Varahamihira
Vijayanandi
Henry Whitehead
Yativrsabha
Yavanesvara
                                   

 

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