The Golden Ratio is one of the roots of the equation $x^2-x-1=0$ and the $n$th Fibonacci number is $F_n=\frac{1}{\sqrt{5}}({\alpha }^n-{\beta }^n)$ where $\alpha$ and $\beta$ are solutions of the quadratic equation $x^2-x-1=0$ and $\alpha >\beta$ hence the many connections between Fibonacci numbers and the Golden Ratio.