Geodesic
The Fibonacci sequence and the golden quadratic
The Teaching of Mathematics, XI (2008) no. 2, p. 85 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The fact that the golden mean ($\Phi=1.61803\dots$) appears both as the limit of the ratio of consecutive Fibonacci numbers, as well as one of the solutions of the golden quadratic, prompted us to conduct a graphical analysis of this equation in order to ascertain what kind of connection its geometry has with the Fibonacci sequence. Our results indicate that the following are all subsumed by the geometry of this equation: the Fibonacci sequence, a sequence of powers of $\Phi$, Division in Extreme and Mean Ratio, $\Phi$, as well as the golden rectangle.
Classification : 00A35 I34 G44
Keywords: Fibonacci sequence, $\Phi$, Division in extreme and Mean Ratio, Golden rectangle. 
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     title = {The {Fibonacci} sequence and the golden quadratic},
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Jose C. Iniguez; B. Argentina Iniguez. The Fibonacci sequence and the golden quadratic. The Teaching of Mathematics, XI (2008) no. 2, p. 85 . http://geodesic.mathdoc.fr/item/TM2_2008_XI_2_a2/