The Science of the Shulba: A Study in Early Hindu Geometry c20.s3.8

c20.s3.8

Did the ancient Hindus recognise the irrationality of √ 2 ? This question does not seem to have troubled Thibaut in any way. For we do not find him to raise it explicitly or to attempt to answer it directly. But it is clear from his writings that he believed in the Hindu knowledge of irrationality of √ 2. Indeed his theory about the discovery of the Hindu approximation to the value of √ 2, which has been quoted in *extenso* before, is fundamentally based on the knowledge of the incommensurability of the diagonal of a square with its sides. Thibaut supposes that the ancient Hindus endeavoured ' to discover a square the side and diagonal of which might be expressed in integral numbers' and then observes, ' undoubtedly they arrived soon at the conclusion that they would never find exactly what they wanted and had to be contented with an approximation.'' Von Schroeder ² and Bürk ³ are more explicitly emphatic. They claim for the ancient Hindus the credit for the first discovery of irrationals. And they have been followed in this respect by Garbe, Hopkins and Macdonell.⁴ But this hypothesis has been criticised and opposed by some modern historians of mathematics.¹