Abstract 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.
