In Search of the Divine Proportion

Reading Time: 3 minutes

phiphiThe summer is drawing to a close, and kids are beginning to get restless as the prospect of returning to school draws near. What better way to enjoy a geekdad-led educational adventure than a hunt for the golden ratio?

The golden ratio is a naturally occurring constant. If A+B divided by A equals A over B, then you have phi, the golden ratio. More simply, it equals approximately 1.6180339887. A rectangle with the proportions of 1 and phi is often called a golden rectangle.

This proportion has fascinated smart people for over two millennia. The reason is a complex one but can be summed up this way: the golden rectangle is by itself considered to have very elegant proportions (for instance, the Parthenon can be broken down into a series of golden rectangles.) More interestingly, and more relevant to this article, golden spirals are found throughout nature.

The golden spiral is a Fibonacci spiral that expands by a factor of phi for every quarter turn it takes. You can overlay golden rectangles over the spiral and it matches perfectly. Guess what? The spiral branches of a tree, the fruitlets of a pineapple, the spines of a pine cone, all follow a golden spiral.

So, summing up the above paragraphs: the beauty of buildings matches the beauty of nature, and it all relates to math. One of the most consistent complaints kids have about math is that they fail to see how it relates to the real world. How many 7th graders have squirmed their way through algebra, unable to understand its relevance? Even math-disinclined kids can appreciate the golden ratio because it directly impacts beauty. Those perfect conch shells? The spiral florets of a plant? A beautiful spiral staircase? It’s all phi, the Divine Proportion. Look for it in your backyard today.

For more information, check out the following books:

The Golden Ratio: The Story of PHI, the World’s Most Astonishing Number

The Golden Ratio and Fibonacci Numbers

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