Mathematics in Ancient and Medieval India c6.s5.34

c6.s5.34

In Babylon, a small cunei-form tablet of the old Babylonian times (c. 1800–1600 B. C.) is now traced in the Yale Babylonian collection (No. 7289) which shows a square with its two diagonals.¹ Three numbers in sexagesimal system are inscribed on it. These three numbers as represented by Neugebauer² as the value of diagonal, a side and the value of √2 (since d = √2 a). Here √2 = 1,24,51,10. Now Hindu³ value √2 = 1 + ⅓ + 1/3.4 - 1/3.4.34, if changed into sexagesimal unit, gives √2 = 1,24,51,10,36…… . This has led to the speculation that the Hindu system of calculating the value of √2 was developed from that of the Babylonians. Two points are important in this connection so far as the Hindu origin is concerned : i) In the period, there was no use of sexagesimal system, ii) the rule was clearly stated thus : "the side of a square is to be increased by its third, the third again by its fourth part less its (fourth parts) thirty-fourth part". We have no evidence of any such method of which the Babylonians were aware. As regards Greek sources, many approximations to the values of √2 were current but such a methood and correct approximation of √2 did not occur.⁴