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The Golden Mean and Golden Bean Chocolate- with High Intergrity Foods
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In philosophy, especially that of Aristotle, the golden mean is the desirable middle between two extremes, one of excess and the other of deficiency.
To the Greek mentality, it was an attribute of beauty. Both ancients and moderns realized that "there is a close association in mathematics between beauty and truth". The poet John Keats, in his Ode on a Grecian Urn, put it this way:
- Beauty is truth, truth beauty, that is all
- Ye know on earth, and all ye need to know.
The Greeks believed there to be three concomitants of beauty: symmetry, proportion, and harmony. This triad of principles infused their life. They were very much attuned to beauty as an object of love and something that was to be imitated and reproduced in their lives, architecture, Paideia and politics. They judged life by this mentality. (From Wikipedia)
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The Golden Ratio
The golden ratio 1·618034 is also called the golden section or the golden mean or just the golden number. It is often represented by a greek letter Phi. The closely related value which we write as phi with a small "p" is just the decimal part of Phi, namely 0·618034.
We can now draw a new square - touching both a unit square and the latest square of side 2 - so having sides 3 units long; and then another touching both the 2-square and the 3-square (which has sides of 5 units). We can continue adding squares around the picture, each new square having a side which is as long as the sum of the latest two square's sides. This set of rectangles whose sides are two successive Fibonacci numbers in length and which are composed of squares with sides which are Fibonacci numbers, we will call the Fibonacci Rectangles. (Learn More)
Fibonacci Numbers, the Golden Section and Plants
One plant in particular shows the Fibonacci numbers in the number of "growing points" that it has. Suppose that when a plant puts out a new shoot, that shoot has to grow two months before it is strong enough to support branching. If it branches every month after that at the growing point, we get the picture shown here. (Learn More)
