Interesting article, Sparteye. Unfortunately, it manages to give an important quality of irrational numbers without really explaining what they are (they are numbers that cannot be expressed as the ratio of two integers) and gives an almost irrelevant quality (its approximate value) of the golden ratio without saying anything important about why it might be considered beautiful.

Try this for a more in depth view of the golden ratio:

http://www.mcn.net/~jimloy/golden.html

In short the golden ratio is the ratio between the sides of a golden rectangle and a golden rectangle is one which, when you remove a square from it, the remaining rectangle has the same ratio between its sides as the original rectangle.