test

The fine-structure constant (α ≈ 1/137) is one of the most mysterious dimensionless parameters in physics. This paper shows that α can be expressed with extraordinary precision as:α ≈ φ / π²,where φ is the golden ratio and π the circle constant. This relation matches the experimental value to within 6 × 10⁻⁹. Within Resonance Theory (R-theory), this identity gains physical meaning: π² represents the fundamental periodicity of wave modes in the zero field, while φ encodes optimal resonance stability. Thus, α emerges not as an unexplained input parameter but as a natural resonance ratio linking geometry and physics.