Aryabhata

Aryabhata (born 476, possibly Ashmaka or Kusumapura, India) was an astronomer and the earliest Indian mathematician whose work and history are available to modern scholars. He is also known as Aryabhata I or Aryabhata the Elder to distinguish him from a 10th-century Indian mathematician of the same name. He is believed to have lived and worked at Kusumapura—near Pataliputra (present-day Patna), then the capital of the Gupta dynasty. Aryabhata is known as the author of Aryabhatiya, composed about 499 ce. A second work, the Aryabhatasiddhanta (also called the Arya-siddhanta), is mentioned by later writers but did not survive as an independent text.

Aryabhatiya

Aryabhatiya is a treatise written in Sanskrit verse particularly popular in southern India, where numerous mathematicians over the ensuing millennium wrote commentaries. The work was written in verse couplets and deals with mathematics and astronomy. Aryabhatiya is divided into four padas (“sections”). The opening pada, “Gitika” (“Verses”), also called “Dasagitika” (“Ten Verses”), comprising ten core verses, sets out basic astronomical parameters, units of time, and numerical constants. It also introduces Aryabhata’s system of alphabetic numeration, in which numbers are represented by syllables formed from consonants and vowels. This system made it possible to encode large numerical values in verse form and was widely used by later astronomers. The remaining padas are “Ganita” (“Mathematics”), “Kalakriya” (“Time Calculations”), and “Gola” (“Sphere”).

Mathematics

In the “Ganita” pada Aryabhata names the first 10 decimal places and gives algorithms for obtaining square and cubic roots using the decimal number system. Then he treats geometric measurements—employing 62,832/20,000, yielding a value of 3.1416, for pi, very close to the actual value 3.14159—and develops properties of similar right-angled triangles and of two intersecting circles.

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Using the Pythagorean theorem, Aryabhata 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.

Astronomy and time calculation

With the “Kalakriya” pada 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).

Did You Know?

India’s first artificial satellite, Aryabhata, was launched in 1975 by the Indian Space Research Organisation (ISRO). The program was overseen by Satish Dhawan, an aerospace engineer who served as chairman of ISRO at the time.

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.

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