Golden Section Search: Optimizing Unimodal Functions via the Golden Ratio — E8 Intelligence Research

FINDING: Golden Section Search is an optimization algorithm that uses the golden ratio (φ ≈ 1.618) to bracket minima of unimodal functions, achieving maximal efficiency by reducing the search interval by a constant factor of φ⁻¹ ≈ 0.618 per iteration. | MATH: φ = (1+√5)/2 ≈ 1.618034; interval reduction factor = 1/φ ≈ 0.618; Fibonacci sequence Fₙ = Fₙ₋₁ + Fₙ₋₂, with Fₙ₊₁/Fₙ → φ as n→∞. The algorithm evaluates two interior points spaced by (φ⁻¹) of the interval, reusing one point from the previous iteration. | CONNECTION: The ratio 0.618 (φ⁻¹) and its complement 0.382 (1 - φ⁻¹) are the fundamental division ratios of the golden section. These same ratios govern phyllotaxis (leaf arrangement) where divergence angles approach 137.5° (2π/φ²), maximizing light exposure and packing efficiency. The algorithm's optimality stems from the same self-similarity property that appears in natural spirals, quasicrystal diffraction patterns, and the golden angle. | DEPTH: 7 — The finding directly links a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com