The Mystery of Mathematical Constants

Pi (), natural constant (), imaginary unit (), golden ratio (), and Euler-Mascheroni constant () are the five fundamental constants constructing all human mathematical and physical systems. For thousands of years, they have been treated merely as abstract computational tools without definite physical origin. Based on the first principles of zero-rest-mass vacuum medium, global angular momentum conservation, and oblate orthogonal bi-elliptic topological primitives, this paper completes the full physical origin decoding of the five constants through rigorous mathematical derivation. represents the geometric skeleton of closed rotating vacuum space; represents the exponential evolution toward minimum-energy steady states under angular momentum conservation; is the physical orthogonal rotation operator of microscopic vacuum dimensions; is the optimal low-dissipation topological growth solution for lossless angular momentum transfer; serves as the topological packing factor bridging discrete microscopic primitives and continuous macroscopic fluid. Correspondingly governing spatial structure, temporal evolution, dimensional transformation, steady-state growth, and multi-scale coupling, the five constants completely resolve the millennium puzzle of mathematical constant origin and accomplish the ultimate closed loop of “all mathematical laws originate from vacuum medium motion”.