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The Golden Ratio

Updated: Dec 18, 2020

You may have noticed that I occasionally mention proportion in my column. It’s an essential ingredient in good design. It is the relationship between the size of one part of an object and another part of the same object.

Take a lamp. A fat shade on a skinny base is out of proportion. Sometimes proportion is confused with scale, which is the relationship between the sizes of two different objects. A 5-foot-wide painting is too large to hang over a 3-foot-wide table. The two are out of scale with each other. But, if you consider the painting and the table as one single scene, then you could say that it is out of proportion. Got it?

Sometimes it’s easy to pinpoint when something is out of whack. Sometimes it’s not, but you “feel” there’s something wrong. On the other hand, when you recognize that something feels right, it is, no doubt, in proper proportion. Have you ever wondered where these feelings came from?

And, why does humankind around the world innately agree? I’ll take a wild guess. I think it’s built into our DNA just like our fight-or-flight instinct. At some point in time, way back, we tuned into the shapes and patterns of the vegetation and animal life around us.

You’ve probably noticed the consistent and rhythmic spirals of nautilus sea shells, pine cones, sunflowers and cauliflower florets. Did these dependable patterns give our early DNA assurance that there was some order, some “rightness,” to the universe – like a cosmic numerical system?

These patterns have actually been mathematically defined, studied and used by ancient mathematicians and architects. Euclid and Pythagoras both obsessed over a certain proportion because of the frequency in which it appeared in geometry.

This proportion is known as the “Golden Ratio” and occurs when a line is divided into two unequal parts so that the longer part, divided by the smaller part, is equal to the whole line divided by the longer part. (How many of you just sketched this out on the nearest piece of scratch paper?) The same formula can be applied to rectangles and triangles.

It’s not important to understand these equations, just to know they exist. In fact, you’ve seen them in action. There’s a reason picture frames are 3-by-5 and not 3-by-4, for instance. The former approximates a Golden Rectangle — and just seems better.

Golden Triangles can be identified in Renaissance art by their centered peaks — like da Vinci’s “The Last Supper” and Michelangelo’s “Pieta.” The Great Pyramid and the Parthenon embody Golden Triangles and Rectangles and are in ideal proportion. Throughout the ages, this proportion has been seen in the works of Plato, Kepler, Mondrian and Salvador Dali. Even Mozart’s musical frequencies can be defined by the Golden Ratio.

I cannot write about proportion without mentioning Leonardo Fibonacci, who, in the 12th century, defined a sequence of numbers such that a number is the sum of the two preceding numbers. Try it: 0, 1, 1, 2, 3, 5, 8. Amazingly, the ratio of any two successive Fibonnaci numbers is very close to the Golden Ratio.

But how do these Golden formulas address our universal consensus of pleasing proportions? Back to nature’s spirals. It turns out that they are Golden, too. To oversimplify, a Golden Spiral, like a nautilus shell, can be formed within a series of nested Golden Rectangles. Our early DNA recognized these Golden patterns, Golden proportions if you will, and has assumed their “rightness” to this day. But I’m just guessing.