Scholars at the Vedic Science Journal have identified early evidence of recursive geometric logic in a 10th-century Sanskrit manuscript discovered in Andhra Pradesh. The text, titled Ganita-Kalpa-Latika, contains a series of verses that describe an iterative method for calculating the area of an ellipse by approximating it through a series of inscribed irregular polygons.
The study demonstrates that these Sanskrit algorithms utilize a precursor to the concept of limits, allowing for high-precision area measurements required for the construction of complex temple foundations and astronomical instruments. The researchers argue that this approach predates similar developments in European geometry by several centuries.
This find suggests that the Deccan mathematical tradition was far more advanced in its treatment of curvilinear geometry than previously understood. The manuscript also includes references to the physical properties of materials, indicating that these mathematical models were directly applied to engineering challenges in the medieval period.