The Geometric Nature of Fundamental Constants: From the 1×1 Triangle to the Discrete Structure of Spacetime

The appearance of the same dimensionless factors in fundamental physics — √2, 1/2, and exponents of −1/2 — is usually regarded as a curiosity or a by‑product of series expansions. This essay develops the thesis that these constants are geometric invariants of a universal discrete △‑structure of spacetime, whose elementary cell is a right triangle with unit legs (△₁×₁). Lorentz transformations, gravitational time dilation, the 4/3 electromagnetic mass problem, and several other physical situations are analysed. It is shown that √2 and 1/2 arise naturally as the ratio of the hypotenuse to a leg and the area of the basic triangle, while the formalism of △‑axiomatics allows known difficulties to be interpreted as manifestations of a gap between the continuous mathematical apparatus and the discrete geometry of reality. Analogies with graphene, quantum information, fractals, and causal dynamical triangulation are provided