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Golden ratio

Two quantities are in the golden ratio if that is the same as the quotient of their sum and the larger of the two quantities

where a > b > 0.

 


Explanation

You can calculate the golden ratio as

With the quadratic formula you get

with as positive solution

and as negative solution

          

As the numbers a and b are both positive, the negative solution is not valid.

 


Additional information

The letter φ (phi) is from the old Greek sculpter Phidias, who wrote a book about the golden ratio.

 


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