GEOMETRIC CONSTRUCTIONS IN KĀTYĀYANA ŚULBA SŪTRA: ANALYZING ANCIENT VEDIC MATHEMATICAL TECHNIQUES

Abstract

This abstract investigates the complex geometric constructs found in the Kātyāyana Śulba Sūtra, an old Vedic mathematical treatise written perhaps 200 BCE. Part of the larger Śulba Sūtras tradition, the text offers sophisticated mathematical ideas mostly concentrated on altar building and sacred geometry. This paper examines Kātyāyana's specialized contributions to geometric problem-solving, especially his approaches for building squares, rectangles, and circles with precise area correlations. Using ancient geometric techniques, the text shows amazing accuracy in approximating irrational numbers—including the square root of 2 and π. Kātyāyana's creative methods for altering geometric forms while maintaining their areas—a mathematical issue fundamental to Vedic ritual requirements especially pique curiosity. The study shows that many of these constructs make use of ideas that correspond with contemporary algebraic ideas, implying a profound knowledge of geometric relations in ancient India. The useful applications of the text in architectural design and ceremonial space organizing emphasize the way theoretical mathematical knowledge is combined with pragmatic geometric ideas. This study shows how religious needs motivated mathematical innovation in ancient civilizations and helps us to better grasp the historical evolution of mathematics in South Asia. The results imply that, given the framework of ancient mathematical successes, Kātyāyana's geometric techniques were more advanced than hitherto known.