Binomial theorem in ancient India

Abstract

The binomial theorem for positive integral exponents was discovered in Europe in the sixteenth century. The triangular array formed by the binomial coefficients undoubtedly played a very important role in the development. The array was known as Pascal triangle (+ A.D. 1665) in Europe. It appeared originally in the work of Apianus (+1527), Stifel (+1544), Scheubel (+1545), Tartaglia (+1556), Bombelli (+1572) and others. The same array was known in China as the 'Old method chart of seven multiplying squares' and appeared at least two centuries earlier in the work of Chu Shih-Chieh (+1303), Yang Hui (+1261) and Chia Hsien (+1100). The paper, apart from early discovery of the theorem in India, shows that the same triangular array was known as meru-prastara in India and occurs several centuries earlier than that of China.