Mathematics in Ancient and Medieval India c8.s2.4

c8.s2.4

The Greek value of π before Archimedes ( c. 250 B. C. ) was not satisfactory. Archimedes' values lie between the fraction 223/71 ( = 3.1408... ) and 22/7 ( = 3.1428... ) which were obtained by the use of 96 sided polygon.² Ptolemy³ ( 2nd century A. D. ) gave an expression for π in sexagesimal unit which is 3°8'30″. This when expressed in fraction gives out 377/120 ( = 3.14166... ) which differs only slightly from Āryabhaṭa I's value of π. It has therefore been suggested by many Western scholars like Rodet¹, Heath² and others³ that Āryabhaṭa I's value was borrowed from Greece. G. R. Kaye⁴, on the basis of Al-Bīrūnī's statement⁵ says that the value given by Āryabhaṭa I occurs in the *Puliśasiddhānta* which was admittedly composed under the Greek influence, supported the above view. The fact that the π values derived from the ratio of the circumference of the earth and its diameter differ substantially from the given values, is also regarded by many of these scholars as a strong argument in favour of the Greek influence on the Āryabhaṭa I's value of π. It should however be pointed out here that the *Puliśasiddhānta* as compiled by Varāhamihira (c. 505 A. D. ), the only available text of the said treatise does not make any mention of Āryabhaṭa I's value, though the other values are given.⁶ Al-Bīrūnī's statement might therefore be based on a recasted edition of *Puliśasiddhānta* whose authenticity cannot be relied upon in preference to that of the Varāhamihira. Then again as already stated above, the Indian workers never calculated their values from the ratio of the circumference of the earth and its diameter. There is therefore no justification for the assumption that Āryabhaṭa I's value was borrowed from Greeks. Needham is also of the same opinion.¹