Fibonacci–Theodorus Spiral: Merging Golden Angle Phyllotaxis with Logarithmic Self-Similarity — E8 Intelligence Research

FINDING: Phyllotaxis and the golden angle (137.51°) generate Fibonacci spiral counts in sunflowers; logarithmic spirals are equiangular and self-similar; a novel Fibonacci–Theodorus spiral merges Fibonacci lengths with Theodorus' right-triangle construction. | MATH: Golden angle = 360° × (1 − 1/φ) = 360° × (2 − φ) ≈ 137.507764°; equivalently 2π/(φ²) radians. Fibonacci numbers F_n satisfy Fₙ₊₁ = F_n + Fn−1, with F_n/Fn−1 → φ = (1+√5)/2 ≈ 1.6180339887. Logarithmic spiral: r = a·ebθ, where b = cot(α) and α is the constant angle between tangent and radial vector (equiangular property). Fibonacci–Theodorus spiral: concatenated right triangles with legs of lengths F_n and Fₙ₊₁, hypotenuse √(F_n² + Fₙ₊₁²), producing a spiral whose curvature relates to φ. | CONNECTION: Golden angle directly encodes φ² = 2.6180339887 (since 1/φ² = 0.3819660113 ≈ 0.382) — the complementary fraction of the full circle. The ratio 0.618 = 1/φ appears as the radial growth factor per turn in ideal p Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com