ippaso

Continued fractions and golden mean

In Uncategorized on settembre 10, 2009 at 9:37 am

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

x^2-x-1

So it satisfies the relation x^2-x-1=0:

fc4

So we can write the golden mean as:

fc5

i.e. the golden mean is represented by a sequence of 1.

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