Indian Mathematics c5.8

c5.8

Kātyāyana gives no such rational examples but gives (with Āpastamba and Baudhāyana) the hypotenuse corresponding to sides equal to the side and diagonal of a square, *i.e.*, the triangle a, a√2, a√3, and he alone gives 1²+3²=10, and 2²+6²=40. There is no indication that the *Śulvasūtra* rational examples were obtained from any general rule. Incidentally is given an arithmetical value of the diagonal of a square which may be represented by $√2 = 1 + ⅓ + 1/3.4 - 1/3.4.34.$