Ancient Indian Mathematics: Sulbasutras – A Mathematical Review

Śulbasūtras, which are compositions from the first millennium BCE, related to the activity of construction of vedis (altars) and citis (fireplaces) for the performance of yajñas (fire sacrifices), constitute a unique historical resource from India from the ancient times, with explicit mathematical content. They manifest familiarity with various geometric constructions and also geometrical principles, including what is now commonly known as Pythagoras theorem. The converse of the Pythagoras theorem played an important role in many of their practical constructions. The task of interrelating the square and the circle in terms of areas was also addressed by them, though in a limited practical context, and the pursuit also seems to have led them to quite an accurate approximation of 2 $$ \sqrt{2} $$ . Study of the Śulbasūtras in the modern framework began in the second half of the nineteenth century, with the work of George Thibaut. Since then four Śulbasūtras, Baudhāyana Śulbasūtra, Āpastamba Śulbasūtra, Mānava Śulbasūtra, and Kātyāyana Śulbasūtra, have been studied by various scholars, to varying degrees of detail. While on the one hand there have been several illuminating findings, on the other hand a variety of poorly substantiated claims and theories have also emerged in historical writings on them. This chapter aims at presenting a reasonably comprehensive account of the mathematical contents of the Śulbasūtras, together with a critical review of various inferences drawn in the literature, and bringing out the issues calling for further studies and clarifications. We highlight also the differences between the different Śulbasūtras and comment on their significance in various respects, an aspect which has not received much attention so far.