by Dr. Rob Strain, DDS AAACD
Have you ever wondered why your eye sees something as pleasing, but in a very similar situation sees something not nearly as attractive? The answer lies in mathematics. There is a mathematical formula the eye uses to find something pleasing in nature, home decorating, the human body or even a smile.
Many centuries ago, Greek philosopher Pythagoras stated the Golden Proportion, Golden Section, or Phi. Phi is the ratio 1.62:1. The rectangle in Figure 1 has sides that are 1.62 times the height. Completing a square inside the rectangle (blue line) creates another vertical rectangle that also has sides that are in the golden proportion. This exercise can be carried on indefinitely.
Our eyes and minds are inherently tuned to enjoy phi structures. In fact, our body structure is an example of phi repeated over and over, such as the relationship of each adjacent bone in our hands.
Leonardo Served Phi at the Last Supper
Phi is seen in classical art, such as Leonardo da Vinci’s “Last Supper,” and sculptor Phidias’ Parthenon statues. In the same way these masters used phi, you can use it to lay out furniture, position paintings on your wall, or in composing and cropping your favorite photographs.
Phi on Your Face
The reason we perceive one person as extremely attractive but a similar face as just ordinary has a lot to do with phi. This attractive dental patient (Figure 2) has a face with many mathematical characteristics that are very close to the golden proportion shown in the drawn rectangles.
Dentists trained in smile design use this knowledge to develop the shape of teeth and the position of the biting edge of the upper front teeth. Finished outcomes can be accurately predicted using computer-generated models for tooth position. Short lower-face heights may be seen in patients with a history of clenching or grinding teeth. Notice the change in chin position in the example shown. The result is a much more attractive face by bringing ratios closer to phi.
Being a Little Off Center Doesn’t Hurt
Perfect symmetry is not a goal for decorators, photographers and most cosmetic dentists. If your eye was drawn to total symmetry, you would set your pictures smack dab in the middle of the wall. Instead, some natural asymmetry is desirable. We like some symmetry — noses on the center of the face or the two front teeth matching perfectly — but straight noses and symmetrical central incisors work best when balanced with a bit of asymmetry. In smile design, the lateral incisors create that balance.
Phi creates balance more than it creates perfection. This balance adds visual appeal. You can take even more pleasure in art, nature, decorating, architecture and your own person as you see phi at work.
Dr. Rob Strain is an accredited cosmetic dentist and professional landscape photographer. He may be contacted through his websites at robstrain.com (dentistry) and wanderluximages.com (photography).
