Phi

Phi, pronounced fi (long i sound), is an irrational number that comes from the equation n2 - n1 - n0 = 0 The solution to this quadratic formula is a number that goes on forever, Phi or 1.618033988... Phi is the basis for a ratio called the golden ratio and this ratio does have the midas touch! The Phi ratio is a pattern that nature follows.  Not only functional and efficient,  it is very pleasing to the eye.  Artists and architects have been incorporating the Phi ratio into their works for centuries.  This ratio has been called the Golden Mean, Divine Porportion, and the Golden Ratio. The Phi ratio can be depicted as a ratio of lengths when the lengths correspond in the following way:

Notice the ratio of the smaller line to the longer line is exactly the same as the ratio between the longer line and the whole line.  Or a+b/a = a/b.

All of these lines are color coded for you to see the golden ratio.  The four lengths of the pentagram's arms are all in golden ratio to each other.

The golden ratio, Phi, is a ratio that is inherent within many natural forms.  It is found in the porportions of the human form, in growth patterns of simple creatures, and even in our solar system.   Click here to explore Phi and Nature

Click here for Phi and Fibonacci

Phi is also a model for artists and architects.  The ratio is found even in ancient times. Click here to study Phi in art and architecture

Johannes Kepler said that Phi is one of "two great treasures of geometry."   (The other is the Theorem of Pythagoras.) Click here to explore Phi and geometry Click here to study about the Pythagoreans

Click here for a YouTube video on Phi

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