One of the great charms of number theory is the existence of irrational numbers—numbers like the square root of 2 or π that can’t be expressed as the ratio of any two whole numbers, no matter how large. The legend goes—probably false, but hey, it makes a point—that the discovery of the irrationality of√2 was so disconcerting to the Pythagoreans, who wanted all numbers to be rational, that they threw the discoverer into the ocean.
Among the mysteries of the irrationals, one number holds a special place: the so-called golden ratio. The golden ratio’s value is about 1.618 (but not exactly 1.618, since then it would be the ratio 1,618/1,000, and therefore not irrational) and it’s also referred to by the Greek letter φ, which is pronounced “fee” if you’re a mathematician and “fie” if you are in a fraternity. If you want an exact description, the golden ratio can be expressed as (1/2)(1+√5.) Source: Slate.com