The gold number

The gold number:

The gold number is the ratio or proportion there is between two segments of lines. It was discovered in antiquity, and can be found not only in geometrical figures, but also in nature. You may find this relationship in various works of art or architecture. For example, the Vitruvian Man, drawn by Leonardo Da Vinci and considered a beauty ideal, is provided as the gold number. What is the origin and significance of this mathematical value?

There are numbers that have intrigued us for centuries. Values ​​such as PI-mathematical ratio of the circumference of a circle to its diameter-usually occur as a result of most diverse equations or proportions of various natural objects. The golden ratio also has many interesting properties and appears hidden and enigmatic, in the most diverse places.

The first to make a formal study on the golden ratio was Euclid, about three centuries before Christ, in his Elements. Euclid defined its value by saying that "a straight line is divided at the end and proportional when the whole line is to the greater segment as the greater the younger." The value of this ratio is a number, as Euclid proved, can’t be described as the ratio of two whole numbers (is irrational and owns infinite decimal) whose approximate value is 1.6180339887498 ...