The Geometric Nature of Fundamental Constants: From √2 and 1/2 to the Discrete △-Structure of Spacetime

In theoretical physics, we often encounter situations where equations “stumble” over seemingly innocuous numerical coefficients: √2, 1/2, or ε⁻¹/². Traditionally, these numbers are regarded as mere consequences of continuous mathematical formalization. We advance the hypothesis that these constants are not algebraic artifacts, but fundamental geometric invariants pointing to the discrete triangular (△) nature of physical reality. Within the RPT paradigm, a direct correspondence is established: √2 appears as the ratio of the hypotenuse to the leg in the basic right triangle △₁×₁, 1/2 as its area, and ε⁻¹/² as a parameter governing the restructuring of the △-lattice of spacetime. This allows us to reinterpret Lorentz’s ether as a universal △-structure and to propose a language of △-axiomatics that bridges the gap between the continuous apparatus of physics and an underlying discrete geometry.