Nemicandra's Rule for Finding the Volume of a Right Circular Cylinder
By Dipak Jadhav
Summary
Dipak Jadhav studies a mathematical rule attributed to the Jaina scholar Nemicandra (10th century) for calculating the volume of a right circular cylinder. In his Jaina canonical texts, Nemicandra states that the volume of a cylindrical solid equals the area of the circular base multiplied by its heightimage/. The article reproduces the original Prakrit verse and provides an English translation. Jadhav explains that the Jaina mathematicians defined the area of a circle using the approximation π = 3 or sometimes 22/7. They measured units like aṅgula and proposed that the volume (v) = πr^2h. Jadhav compares Nemicandra’s formulation with earlier Indian texts such as Aryabhata’s Aryabhatiya and Brahmagupta’s Brahmasphutasiddhanta, noting that although the concept is simple, its explicit statement in Jaina texts demonstrates the sophistication of Jaina mathematicsimage/. The author also comments on how Jaina mathematicians distinguished between plane and solid geometry and used the rule for practical purposes in architecture and ritual altars. A concluding section highlights that by acknowledging Nemicandra’s contributions, historians can better appreciate the breadth of Indian mathematical heritageimage/.
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Conclusion
Nemicandra’s rule v = πr^2h shows that medieval Jaina scholars understood the principle of calculating a cylinder’s volume. Jadhav’s analysis reveals the continuity between Jaina mathematics and broader Indian mathematical traditions and suggests that Jaina texts deserve recognition in the history of geometryimage/.