Study Guide

Ratios & Percentages - The Golden Ratio

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The Golden Ratio

The golden ratio is the most beautiful number we may ever see. We know that sounds a little over the top, but really, everything looks better when the golden ratio is applied.

Architects, painters, fashion designers, and engineers have been using this most illustrious proportion for centuries, because things just look prettier this way.

Mother Nature has been using this ratio for eons when designing proportionate trees, flowers, fruits, shells, and more. If we compare the opposing spirals of a sunflower, a pineapple, or a pinecone, or the ratio of length and width in the growth patterns of a nautilus shell, we'll find that they approximate the golden ratio. Crazy, huh?

So what's the magic number? Technically speaking, the golden ratio, or φ (the Greek letter "phi"), is an irrational number. Say what? For the sake of our brains, we'll define φ as:

(1 + 5^ (1/2)) / 2 = 1.61803398...

An artist uses this ratio when deciding where to put the focal point of a painting, or how far up the canvas the horizon should be. We can even use the two lengths in a golden ratio as the length and width of a rectangle...a golden rectangle. It turns out the golden ratio is a way of proportioning things so they look the best.

Generally speaking, when comparing two quantities like height and width, φ is the ratio that's the most visually appealing. Seriously. Humans are weird like that. Take a look at the following pairs.

Which one looks more right, A or B?

A and B box

       (A Length/ A Width) = 3.87           (B Length/ B Width) =1.61

Which ice cream cone looks more right?

ice cream cones

     (A Length/ A Width) = 1.37    (B Length/ B Width) =1.74

What about these two coffee cups?

coffee cups

      (A Length/ A Width) = 2.10     (B Length / B Width ) = 1.68

If you chose "B" for each, you have a very good eye. The ratio of length to width for each "B" image more closely approximates the golden ratio.

Hey, Nice Face

The golden ratio can often be found right in front of our nose...literally. If we grab a tape measure, we can measure the length of our face from our chin to our hairline and also measure the length from our chin to our nose. The longer length divided by the shorter length may equal 1.618, or the golden ratio, if we have a "perfectly placed" nose. Here are a few more human ratios to try:

length from elbow to wrist/ length from wrist to middle finger tip

length of face/width of face

height/ distance between belly button and foot

Next time you take a walk, look for this beautiful ratio in the world around you!

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