Mathematical Validation of Kalimuthu's Configurations as Degenerate Spherical Manifolds
We provide a rigorous differential-geometric analysis of two spherical configurations proposed by Sennimalai Kalimuthu, where the sum of interior angles of a figure formed by three geodesics on a unit sphere S² attains 360° (2π) and 540° (3π). While such figures satisfy the global Gauss-Bonnet theorem Σθi = π + Area (T...