Posted by: jonglapa | December 15, 2008

The Golden Ratio

I searched “symmetry in everyday life” on Google for symmetry in everyday life, and halfway down the page I saw something about the “Golden Ratio.”  I remember hearing about the Golden Ratio at some point either in a book (was it The Da Vinci Code?) or a math class (but I don’t know which one it would be), and I remember that it is present in several aspects of nature, but, until this, I’d never bothered looking up exactly what the Golden Ratio was.


            Two numerical values, a and b, are said to have the golden ratio if the ratio between a+b over a, the larger value, is equivalent to a over b.  Mathematically:

(a+b)/a = a/b.  Evidently, appearances of the golden ratio abound from the pyramids of Egypt to the Mona Lisa to architecture from ancient Greece to Beethoven’s Fifth Symphony.  Here are some links I came across while looking at some areas in which the golden ratio shows up. explains the golden ratio and the important link of the golden ratio to Fibonacci numbers gives the mathematical and geometrical derivation for the Golden Ratio and the work ancient Greeks did on it shows some examples of Fibonacci numbers in the arts, architecture and music.  



  1. The sixth grade math teacher at my middle school holds a “rectangle beauty contest” every year to teach the golden ratio. She posts five or six differently-proportioned rectangles on a display board for about a week, and at the end of the week, students vote for their favorite. The golden ratio rectangle wins by a landslide ever year. This activity really stuck in my head so I guess it’s a good way to introduce the golden ratio (and its aesthetic appeal)!

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