GOLDEN RATIO IN MATHEMATICS

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What is golden ratio ?

In mathematics, two quantities are in the golden ratio, if their ratio is same as the ratio of their sum to the larger of the two quantities. Let a and b be two quantities such that a > b > 0, then algebraically it is written as follows,




  • Golden ratio is denoted by Greek letter phi given below:



  • The value of golden ratio is,




Golden ratio is a very important concept in mathematics which is used in designing geometrical shapes, in the construction of architectural structures etc.

  • Golden ratio is an irrational number.
  • Other names of golden ratio are golden number, golden section, golden mean, golden proportion, golden cut, divine section, extreme and mean ratio etc.
  • Golden ratio is related to the fibonacci series. If you take any two successive ( one after the other ) fibonacci numbers, their ratio is very close to the golden ratio.



Calculation of the golden ratio

From the definition of golden ratio, we have,


Now,   

From above two equations, 







Therefore,








Multiply the above equation by 𝜑, 







Solve the above quadratic equation, you will get, 






But 𝜑 must be positive because it the ratio of two positive quantities, hence













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