Aryabhatiya

Direct details of Aryabhata's work are known only from the Aryabhatiya.

But Aryabhatiya is the earliest surviving text containing a reference to this basic constant.

Though about half of the entries are wrong, it is in the Aryabhatiya that the decimal place-value system first appears.

In 629 he commented the Aryabhatiya, written in verses, about mathematical astronomy.

Aryabhata, in his treatise Aryabhatiya, is known to have used a similar but more complex system to represent astronomical numbers.

This is an example from Bhāskara's commentary on Aryabhatiya:

The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries.

Aryabhata's most famous work was Aryabhatiya.

He was the author of Karanaprakasa, which is a commentary on Aryabhata's Aryabhatiya.

It is highly likely that the study of the Aryabhatiya was meant to be accompanied by the teachings of a well-versed tutor.

Crowning glory of Aryabhatiya is the decimal place value notation without which modern, mathematics, science and commerce would be impossible.

Aryabhata's Aryabhatiya (499 CE) includes the computation of areas and volumes.

Aryabhatiya-bhashya : Elaborate commentary on Aryabhatiya.

The mathematical part of the Aryabhatiya covers arithmetic, algebra, plane trigonometry, and spherical trigonometry.

In Aryabhatiya Aryabhata provided elegant results for the summation of series of squares and cubes:

The Aryabhatiya: Foundations of Indian Mathematics.

The Aryabhatiya was an extremely influential work as is exhibited by the fact that most notable Indian mathematicians after Aryabhata wrote commentaries on it.

By 499 AD, the Indian astronomer Aryabhata mentioned in his Aryabhatiya that reflected sunlight is the cause behind the shining of the moon.

He had also composed an elaborate commentary on Aryabhatiya called the Aryabhatiya Bhasya.

Eugene C. Clark's 1930 English translation of The Aryabhatiya in various formats at the Internet Archive.

He divides up history astrologically - it is from this exposition that historians deduced that the Aryabhatiya was written in c. 499 C.E.

Indian mathematical works often used word numerals before Aryabhata, but the Aryabhatiya is the oldest extant Indian work with alphabet numerals.

Besides the theories of Aryabhata in the Aryabhatiya and the lost Arya-siddhānta, there is the Pancha-Siddhāntika of Varahamihira.

Several centuries later, the Muslim mathematician Abu Rayhan Biruni described the Aryabhatiya as a "mix of common pebbles and costly crystals".

After Aryabhatiya was translated into Arabic (c. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.