Analytical Emergence of Mathematical Constants

We present the complete analytical derivation of fundamental mathematical constants from a single axiom: space has d = 3 dimensions. Combined with three structural requirements normalization to unity, multiplicative conservation, and informational recursion we show that all constants (e, π, φ,√2,√3, ζ(2), i, γ, the Hertault angle θH, and derived physical ratios) emerge through explicit analytical formulas. The derivation chain is: d = 3 → n! → e → Γ(z) → π → ζ(2) → θH → physics with parallel emergence: d = 3 → Fibonacci recursion → φ and signature → i and UV regularization → γ This establishes that mathematical constants are not arbitrary numbers but necessary consequences of three-dimensional geometry.