Unifying Fibonacci and Theodorus Spirals via Golden Angle Curvature — E8 Intelligence Research

FINDING: The Fibonacci–Theodorus spiral unifies the classical Theodorus spiral (concatenated right triangles) with Fibonacci-number side lengths, revealing a new curvature relation tied to the golden angle. | MATH: Theodorus spiral: vertices at \\(z_n = \\sum_{k=1}^n i \\sqrt{k}\\) (or similar), with side lengths \\(\\sqrt{k}\\). Fibonacci–Theodorus variant: side lengths \\(F_k\\) (Fibonacci numbers), so the \\(n\\)-th triangle has legs \\(F_n, F_{n+1}\\), hypotenuse \\(F_{n+2}\\) (since \\(F_{n+1}^2 + F_n^2 \\approx F_{n+2}^2\\) only asymptotically — exact only for \\(n=1\\): \\(1^2+1^2=2 \\neq 2^2\\); the paper likely uses a modified closure). Golden angle: \\(\\theta_g = 2\\pi(1-\\phi^{-1}) = 2\\pi(2-\\phi) \\approx 137.507764^\\circ \\approx 2.399963\\) rad. Golden ratio: \\(\\phi = (1+\\sqrt{5})/2 \\approx 1.6180339887\\). Related constants: \\(\\phi^{-1} = \\phi-1 \\approx 0.6180339887\\), \\(\\phi^{-2} \\approx 0.381966\\), \\(\\phi^{-3} \\approx 0.236068\\), \\(\\phi^{-4} \\approx 0.145898\\). | CONNECTION: The golden angle is the Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com