Golden Mean Post 1

Golden Mean, Golden Rectangle, Golden Spiral

Golden Spiral

photo taken by Emerald B. edited by Sophia D.

"The golden ratio, which was used by the Greeks, is a “formula” for beauty. It states that the most beautiful object to the human eye is a ratio of 1.618. For example to get this ratio you could have a rectangle with a length of 34 and a width of 21. When you divide these terms you get 34/21, which equals 1.618. These terms are not random however, 21,34 are consecutive Fibonacci numbers. Any two consecutive fibonacci numbers when divided will equal the golden ratio, demonstrating the ubiquitous nature of both the golden mean and the fibonacci sequence. 

A golden spiral, like the one you see above, is not a golden rectangle. Instead, the golden spiral is created by drawing a spiral that fits perfectly inside a golden rectangle. Therefore, it uses a rectangle and the 1.618 ratio to create the most pleasing of spirals to the human eye. For example, draw with your mind's eye a rectangle around the largest centrally located spiral of the 7 spirals on the railing. Begin with a bottom right corner where the spiral meets the "bud" of the flower shape, draw up to the top of the spiral, then left to the edge, down, and right again. The rectangle that you create will have a length and width that when divided will equal the 1.618.

Another method to determine if a spiral is golden or not is to put it inside a golden rectangle and begin to eliminate squares. If you are continuously able to cut off squares and shrink the golden rectangle with the spiral remaining inside, then it adheres to the principles of the golden mean. This method is made possible by the underlying principle that when you chop a square off the end of a golden rectangle, you are left with another golden rectangle. If you continue to do this, your rectangle will get smaller and smaller but remain golden. In other words the golden ratio can be perpetuated in a fractal pattern." 

description by Kyle McNicoll edited by Sophia D.

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