Base-60's Divisor Richness Mirrors Hexagonal Packing in Constructible Polygons — E8 Intelligence Research

FINDING: The base-60 system's power lies in its high compositeness (divisible by 2,3,4,5,6,10,12,15,20,30), enabling exact fractional arithmetic; this directly parallels the constructibility of regular polygons (Gauss-Wantzel) and the hexagonal packing theorem, with a new result showing hexagonal packing patterns inside regular polygons with 6j sides. | MATH: Base-60: 60 = 2²·3·5, τ(60)=12 divisors. Constructible n-gon iff φ(n) is power of 2 (Gauss-Wantzel): n = 2^a·F₁·F₂···Fₖ (Fermat primes). Hexagonal packing density = π/(3√2) ≈ 0.74048 (Kepler conjecture). New result: For regular polygons with σ=6j sides (j≥2), N(k)=3k(k+1)+1 congruent disks pack symmetrically — this is the centered hexagonal number formula (hex numbers: 1,7,19,37,61,...). | CONNECTION: The 6j-sided polygons (6,12,18,24,...) are exactly those whose interior angles are multiples of 60° (base-60 harmony). The packing formula N(k)=3k(k+1)+1 is the hexagonal lattice coordination number sequence — identical to the number Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com