The golden mean is one of the most popular number in mathematics:
Let us study the representation of this number in continued fraction. In a previous post we have seen that any quadratic irrationality has a periodic expansion in continued fraction. So the golden mean has a periodic expansion in continued fraction too. We remember that the golden mean is the root of the equation
So it satisfies the relation x^2-x-1=0:
So we can write the golden mean as:
i.e. the golden mean is represented by a sequence of 1.