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 alternating oscillator around and approximating Phi = Φ. ResearchGate, April 30 2026, DOI: 10.13140/RG.2.2.14424.66568.
Koshy, Thomas Fibonacci and Lucas Numbers with Applications, Volume 1 and Volume 2.. New York: Wiley-Interscience, 2001.

Leonardo da Pisa, Liber abaci, Ms. Biblioteca Nazionale di Firenze, Codice magliabechiano Conv. Soppr. C 1, 2616, fol. 124r Source: Heinz Lüneburg, Leonardi Pisani Liber Abaci oder Lesevergnügen eines Mathematikers, 2. überarb. und erw. Ausg., Mannheim et al.: BI Wissenschaftsverlag, 1993 I Alternate scan: https://archive.org/details/conventi-soppressi-c.-i.-2616/page/n127/mode/1up, https://commons.wikimedia.org/wiki/File:Liber_abbaci_magliab_f124r.jpg#/media/File:Liber_abbaci_magliab_f124r.jpg