The Derivation of the Speed of light using only Geometric Analysis

The speed of light is conventionally defined as a measured quantity requiring clocks and rulers. This paper demonstrates that c can be derived from pure geometry, without recourse to temporal measurement. Starting from the definition of rc—the arc length subtending one degree on the Light circle—we establish the Fundamental Light Equation: c = (180 / π) × 10^12 × rc ... (1) Through a nested circle construction rooted in the Lyman limit wavelength λLy, we prove geometrically that rc = λLy × (180 / π). The electron's spatial extent—a geometric necessity expressed through the fine structure constant α—yields the final expression: c = λLy × (180 / π)^2 × (1 + α / 2π)^2 × 10^12 ... (2) This determines the speed of light entirely from atomic and angular constants—geometry alone, no clocks required. The final formula is a distance in units of length determined by those of the Lyman. This geometric distance determines the fundamental