Vol. 7, Issue 2, Part C (2025)

Aryabhata, India’s greatest mathematicians and astronomers, gave a surprisingly accurate value for π (pi) in his famous book Aryabhatiya. In verse 10 of the Gaṇitapāda chapter, he encoded the value π ≈ 3.1416 that is remarkably close to the true value by using poetic and numerical techniques. This paper offers a modern mathematical reinterpretation of that ancient method. Building on Aryabhata’s original formula, we propose a generalized equation to estimate the circumference of a circle for various radii. Our formula reflects Aryabhata’s style of combining addition, multiplication, and constants in a structured way and introduces a consistent correction factor of 32 to align the result with the standard 2πr formula. This approach demonstrates how ancient Indian mathematical thinking can inspire new insights and methods in modern mathematics. Through historical analysis and numerical validation, this study bridges the gap between classical Indian knowledge and contemporary mathematical modeling.