Emergence of π as a Limiting Invariant from Energy–Charge–Geometry Systems

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This paper proposes a novel conceptual framework in which the mathematical constant π is interpreted not merely as a geometric ratio, but as an emergent invariant arising from normalized physical relationships involving energy, charge, and geometry. By considering systems with circular symmetry and applying appropriate dimensional normalization, it is shown that π naturally appears in the limiting behavior of such systems. This work aims to bridge geometry and physics by suggesting a deeper origin of π rooted in physical structure and symmetry.

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