Consecutive FIBONACCI-number ratios F(n+1) / F(n) as a damped alternating oscillator around and approximating Phi = Φ
Consecutive FIBONACCI-number ratios F(n+1) / F(n) as a damped alternating oscillator around and approximating Phi = Φ by Stefan Geier Because of lim (Fn/Ln) for n to infinite and Fn the n-th FIBONACCI-number and Ln the n-th LUCAS-number the content of GEIER Stefan et al. “Consecutive Lucas-number ratios L(n+1) / L(n) as a damped alternating oscillator around and approximating Phi = Φ“ is correct for FIBONACCI-numbers, too. Therefore we state: Consecutive FIBONACCI-number ratios F(n+1) / F(n) can be interpreted as a damped alternating oscillator around and approximating Phi = Φ . Critique welcome! Refinement welcome! Yours sincerely, Stefan Geier Gerhart-Hauptmann-Straße 6 83071 Stephanskirchen, Haidholzen, Germany, Europe References: Chandra, Pravin and Weisstein, Eric W. "Fibonacci Number." From MathWorld --A Wolfram Resource. https://mathworld.wolfram.com/FibonacciNumber.html . Geier Stefan et al. Consecutive Lucas-number ratios L(n+1) / L(n) as a damped...