Dihedral Group D5 Projection Yields Golden Ratio Convergence in Fixed-Point Iteration — E8 Intelligence Research

Abstract

FINDING: Dihedral group D5 projection yields golden ratio convergence rate in fixed-point iteration, linking group symmetry to harmonic ratio. | MATH: Fixed-point iteration convergence rate for D5 projection is φ = (1+√5)/2 ≈ 1.618; inverse golden ratio φ⁻¹ ≈ 0.618; dihedral group D5 order = 10, generated by rotation of 72° (2π/5) and reflection. | CONNECTION: D5 symmetry directly encodes pentagonal geometry; golden ratio emerges as eigenvalue of D5 rotation matrix; 0.618 = φ⁻¹ = 2/(1+√5); 0.382 = φ⁻² = (3-√5)/2; 0.786 = √φ⁻¹ ≈ √0.618; 2.618 = φ² = (3+√5)/2. | DEPTH: 8 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com