The Golden Ratio and the Fibonacci Numbers defined
The History of the Golden Ratio
The History of Fibonacci
Mathematical Properties of the Golden Ratio
Constructing a Golden Rectangle
The Secret of the Golden Ratio
The Golden Ratio and Beauty...
What is the Golden Ratio?
The Golden Ratio is a unique number, approximately 1.618033989. It is also known as the Divine Ratio, the Golden Mean, the Golden Number, and the Golden Section. Its unique mathematical properties have resulted in a very long and influential history.
What is the Fibonacci Sequence of Numbers?
The Fibonacci numbers are a unique sequence of integers, starting with 1, where each element is the sum of the two previous numbers. For example: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.
Relationship Between the Fibonacci Sequence and the Golden Ratio
The Fibonacci Sequence is an infinite sequence, which means it goes on for ever, and as it develops, the ratio of the consecutive terms converges (becomes closer) to the Golden Ratio, ~1.618. For example, to find the ratio of any two successive numbers, take the latter number and divide by the former. So, we will have: 1/1=1, 2/1=2, 3/2=1.5, 5/3=1.66, 8/5=1.6, 13/8=1.625, 21/13=1.615.
As we can see, the ratio approaches the Golden Ratio, which is also known as the Golden Section and Golden Mean. Even though we know it approaches this one particular constant, we can see from the graph that it will never reach this exact value.