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

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.

本文提出一种新颖的概念框架，将数学常数π不仅视作几何比值，更视为由能量、电荷与几何构成的归一化物理关系所催生的涌现不变量。通过考量具有圆对称性的系统并施以恰当的量纲归一化操作，本文证明π会自然地出现在此类系统的极限行为中。本研究旨在通过揭示π根植于物理结构与对称性的深层起源，搭建起几何学与物理学之间的桥梁。