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 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. The work was written in verse couplets
and
deals with mathematics and astronomy. Following an introduction that contains
astronomical tables and Aryabhata’s system of phonemic number notation in which
numbers are represented by a consonant-vowel monosyllable, the work is divided into
three sections: Ganita (“Mathematics”), Kala-kriya (“Time Calculations”), and Gola
(“Sphere”).
View of the Andromeda Galaxy (Messier 31, M31).
Britannica Quiz
Astronomy and Space Quiz
In Ganita 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 (= 3.1416) for π, very close to the actual
value
3.14159—and develops properties of similar right-angled triangles and of two
intersecting
circles. Using 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 ,
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.
