FINDING: Golden ratio appears in quantum dimensions of exceptional Lie algebras and Coxeter numbers, notably in E8 root system projections. | MATH: Quantum dimension formula for E8 at level 1: \ (d = (/30) (/5) 1. 618 \) (golden ratio). Coxeter number h=30 for E8; ratio of Coxeter numbers h (E8) /h (E6) =30/12=2. 5, not golden. However, the ratio of certain root system angles yields φ: e. g. , dihedral angle in E8 projection to 2D gives φ-based tiling. | CONNECTION: Golden ratio φ=1. 618, its reciprocal 0. 618, and φ²=2. 618 appear in E8 root system symmetries and the "Magic Star" projection (Michael Rios). The E8 root system has 240 roots; its projection onto a 2D plane using Coxeter plane yields a 30-fold rotational symmetry (Coxeter number 30) with φ ratios between radii of concentric rings. This links to icosahedral symmetry (h=30 for icosahedron) and quasicrystalline patterns. | DEPTH: 8 — Profound connection between exceptional Lie algebras (E8), golden ratio, Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Mon,) studied this question.