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Sunday, July 3, 2011

The Golden Mean

There are forces and consistencies in nature – we call them the Laws of Nature - that have shaped the evolutionary processes to produce everything that we see in our environment on Earth. The golden mean is a ratio [rounded off it is 1.618] that is one such consistency. It mysteriously defines the proportions of the branching in plants and the bones in an animal's skeleton as well as a myriad of other natural phenomena!
It appears we humans are predisposed by nature to be somehow attuned to the golden mean and using it ourselves seems to make our architectural and artistic creations more harmonius. If given a choice about what we see as the most pleasingly proportioned rectangle for instance, we choose the one whose ratio of length to width is closest to the golden mean. A simple example would be a rectangle whose length is 1.618 units and width is 1. Obviously dividing the length by the width gives the golden ratio. If you click on the word video, the first part particularly will you give a sense of the remarkable properties of this ratio.

It was the Greek mathematician Euclid who first geometrically defined the ‘golden mean’ or ratio and started the recognition of it as an all-pervasive, and recurring number in nature.

In 1202 an Italian mathematician, Fibonacci, when playing around with a simple series of numbers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 … , happened on a connection to the golden mean. If you divide any two neighboring numbers in the series, the larger one by the smaller one, you will get the golden ratio and if the smaller number is divided by the larger one you get 0.618 which is the golden mean minus 1.

If you click on this site, you’ll see it is pretty amazing how Fabonacci's numbers play out so often in nature – but not always. On occasion another series is followed. As you watch the videos and search the internet, I hope you can appreciate how naturally scientists in studying their environment, come up with the beautiful mathematical relationships and and equations – some easy like the golden ratio and some comprehensible to only a few. Rie

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