Analysis of information sources in references of the Wikipedia article "阿耶波多" in Chinese language version.
Aryabhata himself (one of at least two mathematicians bearing that name) lived in the late 5th and the early 6th centuries at Kusumapura (Pataliutra, a village near the city of Patna) and wrote a book called Aryabhatiya.
Aryabhata gave the correct rule for the area of a triangle and an incorrect rule for the volume of a pyramid. (He claimed that the volume was half the height times the area of the base.)
He gave more elegant rules for the sum of the squares and cubes of an initial segment of the positive integers. The sixth part of the product of three quantities consisting of the number of terms, the number of terms plus one, and twice the number of terms plus one is the sum of the squares. The square of the sum of the series is the sum of the cubes.
