Golden number

The golden number is the value of a certain proportion or ratio between two quantities of the same nature such as two lengths, two angles, two numbers of branches etc.

This number, like "pi", is irrational. Its symbol is "phi" (from Phydias). Its value is given by the solution to the second degree equation x² - x - 1 = 0 of which the roots are: (1+/- root 5) / 2 = x= 1.61803... and x' = - 0.61803...= - 1 / x .

Any Fibonacci series can be used to find the golden number to at least 2 decimal places from the seventh or eighth number onward. You would have to take the series to infinity to find the exact figures.

In geometry too, the golden number can be found in any regular pentagonal shape and in a 5-pointed star, and in the logarithmic or Archimedean spirals and certain specific patterns.