Indian values for \(\pi\) derived from Āryabhaṭa’s value. (English) Zbl 0677.01003

In this paper the authors demonstrate that Āryabhaṭa’s value of \(\pi\), expressed by the ratio 62832/2000, was very influential in the history of Indian mathematics, and that several other ratios, eg. 22/7, 355/113, 600/191, can be derived from Āryabhaṭa’s. They also show that the strange formula, \(C=3d+(16d+16)/113,\) which is given by the Jaina mathematician Vīrasena, can be explained as an attempt to make the ratio 355/113 closer to Āryabhaṭa’s. In the Appendix of this paper two convenient lists of values of \(\pi\) attested in the Sanskrit literature are given, one in chronological order and the other in numerical order. The bibliographical information is also very useful.
Reviewer: M.Yano


01A32 History of Indian mathematics