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.

 

http://www.goldenratio.org/info/index.html#spaceandtime explains the golden ratio and the important link of the golden ratio to Fibonacci numbers

 

http://community.middlebury.edu/~harris/Humanities/TheGoldenMean.html gives the mathematical and geometrical derivation for the Golden Ratio and the work ancient Greeks did on it

 

http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibInArt.html#mozart shows some examples of Fibonacci numbers in the arts, architecture and music.  

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Responses

  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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