One of the advantages of getting FOY^{®} Dentures is that it allows you to get a completely new smile. No matter what your smile looked like before, you now have the opportunity to get an attractive smile. In designing your new, attractive smile, there are many potential approaches to designing it. One that we like to utilize is the Golden Ratio, also called the Golden Proportion, a mathematical relationship often found in nature that helps us to create an attractive smile.

## What Is the Golden Ratio?

The Golden Ratio is a mathematical relationship in which the ratio between the sum of two numbers and the larger of the two numbers is the same as the ratio between the numbers. In an equation, this looks like (a+b):a=a:b. In this formulation, if a is 1, then b is approximately 0.618.

You can also define the Golden Ratio by using the Fibonacci sequence. The Fibonacci sequence is defined as a sequence in which each term is defined as the sum of the previous two terms, starting with 0 and 1. So the first seven terms in the sequence are 0,1,1,2,3,5,8. You can see how the ratio begins to converge on the Golden Ratio. The ratio 3:2=1.5, 5:3=1.67, 8:5=1.6. So you can see although it bounces back and forth it gets closer and closer to the number, and a few terms later we have 55:34=1.618.

## The Golden Ratio in Nature

There are many places that we see the Golden Ratio in nature. One of the most commonly cited examples is the spirals of seeds in a pine cone. These seeds tend to fit together in spirals that correspond to a Fibonacci sequence, such as 8 one way and 13 the other way. Flower petals often (but not always) conform to a Fibonacci number. Mathemusician Vi Hart has a good video series about Fibonacci spirals, and you can find more examples in this article.

The Golden Ratio is even found in your smile.

## The Golden Ratio in Your Smile

There are basically two places where the Golden Ratio might be found in your smile. One is in the ratio of the height of your teeth to the width. We know this creates a pleasing proportion, although we’re not sure if it’s found in nature. This is hard to measure and verify because the height of your teeth changes with wear.

However, it’s easy to track in the width of your teeth. According to the hypothesis, the visible width of your central incisor to your lateral incisor and the lateral incisor to the canine should both be governed by the Golden Ratio. This holds up pretty well in natural smiles–being found more in attractive smiles than in unattractive smiles–and we know that it creates an attractive artificial smile for your dentures.