April 27th, 2004

The Divine Ratio

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The most fascinating part about Dan Brown’s The Da Vinci Code is the emphasis on PHI – The divine ratio or in simple numerical terms: 1.618… This number, existed in almost all the secret societies in the ancient world and today the focus has shifted toward it modern successor – the PI or 3.142. PHI, on the other hand is much more complex and as you unwind the mysteries of the number, it continues to amaze you. I have always loved a semblance of order amid chaos and no chaos can be more chaotic than nature itself. To discover that even in nature, there exists an underlying template is almost akin to discovering the concept of God. The easiest way to describe PHI is to talk about the famed Fibonacci Series.

The Fibonacci Series is just another way to derive PHI, named for the Renaissance Era Italian who rediscovered this mathematical principle. In this number series, each number is the sum of the preceding two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… Any number in this series divided by its preceding number is a ratio that gets closer and closer to PHI as the numbers get larger and larger. It can be best described visually by the accompanying visual image of a PHI spiral. “Fibonacci’s Summation Series creates a PHI spiral—the universal form used in Nature—from flowers to cyclones to galaxies—pattern and proportion of living, growing things. Whirling bodies emit particle trails and wave energy tails like the PHI. In biology, a plant unfolds its leaves in Fibonacci intervals. The PHI spiral is the geometry of growth”.

Get a little more creative when you are alone in the bathroom. Measure your height and divide it by the distance from the belly button to the floor. You get – yup, the PHI. The examples are endless; from the proportion of female bees and male bees in a colony, petal arrangements of roses, the breeding patterns of rabbits and the shape of our galaxy. Phi is also claimed to have been crucial in the design of the Great Pyramids, the composition of the Mona Lisa and the construction of Stradivarius violins. Leonardo Da Vinci, almost celebrated as God in Dan Brown’s classic novel regularly used the PHI in his paintings. I have been utterly fascinated by this number and am just beginning to explore its endless connections.

Try this puzzle: Elvis can climb stairs one at a time or two at a time. This means he can climb a flight of, say, four stairs in five different ways: 1-1-1-1; 1-2-1; 1-1-2;2-1-1;2-2. How many ways can Elvis climb a flight of, say n stairs? Why in the heck do I mention this puzzle? A special treat for the ones who guess it.

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