The Remarkable Relationship Between the Fibonacci Numbers and the Golden Ratio

You can derive the Golden Ratio from the Fibonacci numbers and you can generate the Fibonacci numbers from the Golden Ratio

The Golden Ratio — also know as the Divine Constant — is a fascinating natural constant. It occurs across many fields of mathematics and science and can be represented in many ways. The easiest way to describe the Golden Ratio is to take a line segment and divide it into two sections, such that the ratio of the entire line segment to the larger section is the same as the ratio of the larger section to the smaller section. That ratio is the Golden Ratio. This picture may help:

One of the most common way of representing The Golden Ratio is the unique positive solution to this equation:

Some simple algebraic manipulation and the use of the formula for quadratic roots renders the golden ratio to be (1 + √5)/2. This is an irrational number approximately equal to 1.618.

There are many other ways the Golden Ratio can be represented. One commonly known approach is the limit…