## Aryabhatta: The Great Mathematician

Aryabhatta wrote the **Aryabhatiya**, a 121-verse manuscript (476-529 A.D.). He invented methods for arithmetic, geometry, algebra, and trigonometry in addition to astronomy. Also calculated the value of the 'pi' to be 3.1416 and talked about mathematical concepts like numerical squares and cube roots.

Through sine functions, Aryabhata is credited with developing trigonometry.

### Background

Aryabhatiya was particularly well-known in South India, where it influenced a number of mathematicians in the subsequent era. This poem, written in poetry couplets, is on mathematics and astronomy.

Following an introduction that includes astronomical tables and Aryabhata's vowel number notation system, the book is divided into three sections.

Ganita (mathematics)

Kala-kriya (time calculations)

gola (philosophy, sphere).

**Ganita:** Aryabhata defines the first ten decimal places in ganita and explains how to use the decimal number system to calculate square and cubic roots. He then discusses geometric measures in addition to the properties of two intersecting circles and identical right-angled triangles.

Aryabhata also discovered a method for constructing a sin table using Pythagoras' theorem.

Additionally, mathematical series, quadratic equations, compound interest ratios and proportions, and solutions to various linear equations are all included.

Bhaskara I named Aryabhata's general solution for linear indeterminate equations kuttakara ("pulveriser") because it involved decomposing the problem into smaller and smaller problems with decreasing coefficients, a process analogous to the Euclidean algorithm and also related to the method of continued fractions.

**Kala-kriya:** Aryabhata then studied astronomy, with an emphasis on the planets' motions along the ecliptic.

Among the subjects covered are time definitions, eccentric and epicyclic models of planetary motion, planetary longitude corrections for various terrestrial locations, and a theory of "lords of the hours and days" (an astrological concept used for determining propitious times for action).

**Gola:** Aryabhatiya concludes gola with spherical astronomy, in which he demonstrates how to apply plane trigonometry to spherical geometry by projecting points and lines on the surface of a sphere onto appropriate planes.

Solar and lunar eclipses are predicted, and the apparent westward movement of the stars is explained explicitly as a result of the spherical Earth rotating about its axis.

Aryabhata also correctly identified reflected sunlight as the source of illumination for the Moon and planets.

During Iran's Sasanian period, Aryabhatasiddhanta had a significant influence on the development of Islamic astronomy. Its contents were preserved in part through the writings of **Varahamihira, Bhaskara I, and Brahmagupta**.

It is one of the earliest works of astronomy, establishing midnight as the start of each day.

### Varahamihira

Varahamihira lived in Ujjain and wrote the Panchasiddhan Tika, Brihat Samhita, and Brihat Jataka, among other works. Five early astronomical systems, including the Surya Siddhanta, are summarised in the first chapter. A