Golden Angle and Fibonacci–Theodorus Spiral Unify Plant Phyllotaxis — E8 Intelligence Research

FINDING: The golden angle (≈137.507764°), derived from the golden ratio, governs phyllotaxis (leaf/flower arrangement) and produces Fibonacci spiral patterns in plants; a new Fibonacci–Theodorus spiral extends this to concatenated right triangles. MATH: - Golden angle: \( θ = 360^∘ × (1 - 1/φ) = 360^∘ × (2 - φ) = 360^∘ / φ^2 ≈ 137.507764^∘ \), where \( φ = (1+√5)/2 ≈ 1.6180339887 \). - Equivalent: \( θ = 2π / φ^2 \) radians. - Fibonacci recurrence: \( Fₙ₊₁ = F_n + Fₙ₋₁ \), with \( F_1 = F_2 = 1 \). - Phyllotaxis condition: successive primordia are placed at angle \( θ \) from previous; the continued fraction of \( θ/360^∘ = 1/φ^2 = [0;2,1,1,1,…] \) ensures maximal packing efficiency. - Fibonacci–Theodorus spiral (arXiv:2407.07109): triangle side lengths \( F_n \), hypotenuse \( √{F_n^2 + Fₙ₊₁^2} \), spiral angle increments \( (Fₙ₊₁/F_n) → (φ) Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com