Written by  //  February 13, 2011  //  TIMES  //  No comments


Phi Φ is a Greek letter that represents an idea: the proportion 1 to 1.618. What is unusual about this proportion or idea is that it naturally occurs in the physical world and also as a product of subconscious human intuition.

Here is an example of Φ occurring in the physical world:

 The human body is proportioned such that the shorter segment of the leg (the calf) can be given a value of 1 and the corresponding value of the longer segment (the thigh) will approximate the value of 1.618. Interestingly enough, if the longer segment of the leg (the thigh) is then valuated as 1, the corresponding value of the length of the entire leg will approximate the value 1.618. The same is true of the arm and its segments and of the teeth, starting with either of the two top front teeth and moving out. This relationship is also found if the body is divided at the naval or if you determine the position of the lips between the bottom of the nose and the bottom of the chin. You’ll also find that your eyes divide the head lengthwise in this same proportional fashion. Even the digits of the fingers can be found to approximate this proportion. The list goes on.

Leonardo da Vinci illustrated this concept in his famous rendering The Vitruvian Man:

The proportion is also represented in the Fibonacci Sequence and the Fibonacci Spiral, as seen here, naturally occurring in the physical world, both as a product of the dynamics of motion and biological development:

My interest in Φ began when I was about 18 years old. I saw a documentary about appealing proportions of the face being related to beauty. Subsequently I was delighted to find out that dentists employ what is called a dual-gauge caliper to help them measure out the proportion. Even though it cost $100, I was eager to purchase one:

 To use this device, you simply set either of the caliper widths to a given length and the other caliper width will automatically adjust to the appropriate proportion 1:1.618. I believe the actual name of this device is the “Golden Mean Gauge.” Golden Mean is another term for Φ.

 I began using my Golden Mean Gauge to measure all sorts of everything and was delighted to discover that Φ  is everywhere. Humans are so connected to this proportion that they even intuitively and subconsciously imbue their artwork with Φ. See if you can find Φ in these seemingly drab, yet world-renown paintings:

 Or how about Φ in these buildings?


Here’s a beautiful little video about Φ in nature, as well:


If you’re interested, there’s even a nice little book about Φ called The Divine Proportion: Φ PHI In Art, Nature, and Science.

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