What is the Phi Factor?

I have a math tattoo.  Really, I do.  I’ll let that sink in for a second.  (It is, perhaps, a bold thing to admit to the world, though I’m not sure if admitting I have a tattoo is the bold part or admitting that it is a math symbol what is truly gutsy).  It is a tattoo of a Fibonacci spiral on my right shoulder blade, oriented vertically.

For those of you unfamiliar with the Fibonacci spiral, it is a logarithmic spiral whose growth factor is the golden ratio, often referred to as phi (φ).  That is, the spiral gets wider by a factor of φ for every quarter turn it makes.

You probably recognize it from the shape of a conch shell or the pattern of seeds in a sunflower.  It’s called the golden ratio because it is the most perfect and most beautiful ratio, or proportion, in nature.  It’s the ratio of your height divided by the distance from your waist to the ground.  Or the proportions of the Pantheon’s facade.  It’s found in Leonardo da Vinci’s Vitruvian Man and in the placement of the climax of Frederic Chopin’s Etudes and Nocturnes.  This irrational number (that is, cannot be expressed as a fraction of two non-zero integers) seems to pop up everywhere, and in doing so highlights connections between art, mathematics, nature, music, you name it.

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