நாட்டியத்தில் கணிதம்: தாளக்கட்டுகள் மற்றும் ஜதிகளில் பொதிந்துள்ள கணித நுணுக்கங்கள் பற்றிய ஆய்வு

This research delves into the profound intersection between the Indian classical dance form, Bharatanatyam, and mathematical principles. While dance is often perceived purely as an aesthetic expression, its structural foundation—Thala (rhythm) and Laya (tempo)—is built upon rigorous mathematical precision. This study specifically explores the roles of Arithmetic, Permutations and Combinations, and Geometry in the formulation of 'Thala structures' and 'Jathis'. The research explains how the fundamental units of movement are divided based on time measures and analyzes the numerical transformations involved in creating different 'Gatis' (rhythms) such as Chathusram, Thisram, and Misram. The composition of Jathis is logically analyzed to show how a specific number of 'Matras' (beats) can be achieved through various mathematical combinations. For instance, the 'Thirikalam' (three speeds) used in Teermanams strictly adheres to the rules of multiplication and division. Furthermore, the study touches upon how the angles and postures (such as Aramandi) maintained by a dancer align with Euclidean Geometry. In conclusion, this research establishes that Bharatanatyam is not merely an aesthetic art form but a logical 'dancing mathematics' that translates abstract numbers into visual patterns.