The Geometric Nature of Fundamental Constants: From the 1×1 Triangle to the Discrete Structure of Spacetime
Year: 2026
Type: article
Abstract: 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
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171258663
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