Why is the golden ratio important?

It's important because it is found (or appears to be) in so many areas of life, most notably in nature, and most importantly in mathematics. The Fibonacci sequence and the concept of fractals (like the infinitely divisible golden rectangle) are great examples of this. Ancient Egyptian and Greek architects built many of their structures with this ratio in mind. Philosophers see this ratio as having an important significance, since it occurs in nature so often.

A lot of people believe that this formula, known as the golden ratio or phi (φ) pops up in everyday life. The truth is that it does not actually appear in the places it is said to. Many claims of its occurrence are false.