The golden ratio was first recorded and defined in written form around 300 B.C. by the Greek mathematician Euclid in his major work "Elements." It is believed that the ancient Greeks may have used the golden ratio to determine the proportions of the golden rectangle in their architecture, such as in the dimensions of the face of the Parthenon, which predates Euclid's "Elements" by more than 100 years. Some scholars, however, disagree with the premise that the specific mathematical ratio was consciously used as a component of architectural design prior to Euclid's written definition of it.
The golden ratio refers to a specific ratio between two numbers which is the same as the ratio of the sum of those numbers to the larger of the two original quantities. This can also be expressed as "a plus b is to a as a is to b" assuming that "a is greater than b and b is greater than zero." The value of the golden ratio is an irrational number, which is 1.6180339887...., and is often represented by the Greek letter "phi." Because the geometric shapes and designs whose proportions exhibit this ratio appear pleasing to the eye and are frequently found in nature, the golden ratio has also been called the "divine proportion." Euclid referred to it as the "extreme and mean ratio."
The golden ratio appears in connection with the Fibonacci sequence of numbers first introduced to Europe by the 13-century Italian mathematician of the same name in his book "Liber Abaci." The Fibonacci sequence consists of a series of numbers in which each quantity is the sum of the two that precede it. As the sequence progresses, the result derived by dividing a number by the one before it will be progressively closer to the golden ratio.