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The golden ratio is a number, commonly known as phi, defined as 'phi * phi = phi - 1.'  The value of phi is

The golden ratio is a number, commonly known as phi, defined as 'phi * phi = phi + 1.'  The value of phi is

:<math>\frac{1 + \sqrt{5}}{2}</math>  

:<math>\frac{1 + \sqrt{5}}{2}</math>  

:1.618...  

:1.618...  

It has been observed that the golden ratio is evident in the arrangement of branches along the stems of plants, and of veins in leaves.

It has been observed that the golden ration is evident in the arrangement of branches along the stems of plants, and of veins in leaves.