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Phi: the Golden Ratio

November 18, 2009

Brit Trogen

One of the most mysterious occurrences in the natural world can be summed up in a single number: 1.6180339887.

Granted, it's not the simplest number out there, and it doesn't spell anything funny when you turn it upside down on your calculator (I tried). Mathematically, it occurs when the ratio of two lengths adhere to the following rule:

And while it might seem like a simple mathematical relationship, this number, also called phi (φ), turns up inexplicably in nature.

It's the ratio of your forearm to your hand. Thorax length to abdomen in bees. Seed spirals in flowers, and length to width for a single groove of a DNA helix. The adjacent spirals in a nautilus shell, and the rings of Saturn, and the physics at work in a black hole.

So how or why does this enigmatic number show up in so many evolutionary and physical forms?

One biological theory is that it's the most perfect representation of beauty. And in fact, this is an idea that artists, architects and plastic surgeons have been using for years. Consider Leondardo's Vetruvian man, often viewed as the perfect representation of the human form. Or the fact that a mask constructed of golden ratio features is believed to make the ideal human face.

For me, the existence of Phi is both creepy, and sort of comforting. It's almost as if we're all connected by this bizarre ratio, from the smallest molecules to the farthest reaches of the cosmos. But in the end, try as we might, it's impossible to find a rational explanation for it.

It is an irrational number, after all.

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