Physical Beauty and the Fibonacci

Why we perceive some physical things as beautiful and not others can seem mysterious, but when we examine how we determine beauty, it may not be so mysterious after all.  In fact, beauty is greatly influenced by simple mathematics, strange as that may seem!

Before we get to the mathematics of beauty, there is something underlying it all.  A couple of years ago, an experience enlightened me on why people often perceive beauty the way they do.  I was building a house on spec (not pre-sold) so I had to choose interior paint colours.  Always looking for something that might interest potential buyers over competitive offerings, my interior designer suggested some colours that were very popular in Vancouver, BC.  I thought it made sense to try that here in the Rocky Mountains, so we went with her suggestions for the main floor, while doing the upper floor in colour tones which had previously proven popular. The upper floors were earthtone colours while the main floor tended toward blue.  When it came time to show the finished home, I listened very carefully to visitors and their reaction to the colours.  Of course most people are too polite to say they don’t like something, but when many specifically stated they loved the upstairs colours but said nothing about the main floor, I realized I made a big mistake on the blue colours, even though I didn’t know why at the time.  I repainted the main floor and the reactions greatly improved!  Why?  A year or two later it dawned on me that people love to be in harmony with their environment.  What they see around them in nature is what informs them of beauty and they want harmony with it…..all quite sub-consciously.  Where we live, there are lots of earthtones of browns, greens, even grays in the mountains, and those are the colours that put people in harmony with nature.  In Vancouver, right on the ocean, blue is the colour of nature and as a result, very popular.

So if nature informs us of beauty, then why are some architectural shapes more beautiful than others?  Why does the shape of a painting enhance the beauty of the picture?  Why are some faces and body shapes considered more beautiful than others?  It actually relates to a simple number sequence that occurs in nature over and over again.  We visually see this sequence and its proportional ratios, and this becomes considered beauty to us, as it is in harmony with nature.

Mathematically, here is the sequence: 1,2,3,5,8,13,21,34,55,89,144…..and so on, where the current number is always added to the one before it. As the numbers get larger, this sequence produces a ratio of approximately 1.62 (or inversely .62). This sequence is called the “Fibonacci” and the ratio of 1.62 is the “Golden Ratio.”

Here are someimages examples of the sequence and ratio in nature:

shells hurricanes-galaxies plants

Here is how the ratio shows up in the body construction:

imgres ArmGoldenRatio images Fibonacci Human Body

How about in art and architecture?

tn_Mona Lisa Golden section tn_golden-parthenon

An artist will not only make sure the dimensions of the picture are in the Golden Ratio, but they will place the primary subject in the Fibonacci spiral:

tn_golden_ratio tn_1559da21eb35ac10daff32b5a43e5ebd9f37f8-001


So if you are trying to figure out the right size of a picture frame or the right shape of a window, use the 1.62 ratio formula for a rectangle and you will get a shape that will be pleasing to the eye, almost magically! (although it’s actually quite scientific)



What about beautiful faces and “correctly” proportioned bodies?  The Golden Ratio is all over that.  Here is Jessica Simpson, considered as having an exceptionally beautiful face which has numerous points of the 1.62 ratio on it:


Body shape in Western culture indicates that the “ideal” chest to waist ratio for women is about 1.45, and similarly for men’s shoulders to waist ratio but as the ratio gets closer to 1.62, the more attraction it gains.  Hence, the big workouts for men that flatten the abs and pump up the bi/triceps and shoulder muscles while surgeons are kept busy with waist liposuction and chest augmentation procedures…..all in the pursuit of the Fibonacci ratio of beauty!

In a sense, nature has overwhelmed us in convincing of how we should perceive physical beauty.  Our drive for harmony with nature is pervasive.   On the other hand, our drive for social harmony is found through “inner beauty”, but I’m not sure yet how the Fibonacci influences that!


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