## The Golden Ratio: The power of attraction

Complexity level:
8
Project cost (\$):
Time required:
Additional time is needed to prepare materials and recruit participants.
Material availability:
Safety concerns:

### Abstract

Our attraction to others may be rooted more in math than in a beautiful smile or pretty eyes. The Golden Ratio is a theory based on the ratio of dimensions of facial features in relation to the dimensions of the face. In this science fair project, you will determine the effects of the Golden Ratio by having participants view photographs of faces and rate their attractiveness.

### Objective

Test the validity of the Golden Ratio.

### Background

The golden ratio is a mathematical formula that appears to explain why we find objects aesthetically pleasing based on the proportion of 1.618. For example, if you were to measure the length of your head from the top of your head to the bottom of your chin, as well as the width of your face, and divide the sum of these two figures by the larger figure, your face would typically fit the Golden Ratio. The Golden Ratio can be found throughout nature and is frequently used by plastic surgeons to determine the best dimensions for our faces.

Golden Ratio

### Materials

10-16 photos of people's faces, minimum dimensions 5" by 7," half of which should depict males and the other half females.
• 10 participants (five males and five females. Age of the participants should be close to the ages portrayed in the photographs).
• Pen or pencil
• ### Procedure

Pre-experiment

Obtain five to eight headshots (or portraits photographs) of males and an equal number of headshots of females. The headshots should be a minimum of 5 inches by 7 inches so that you can clearly see the facial features. Sources of photographs can be:

• Magazines
• Internet
• Photos you have taken yourself.

Assign a number to each photograph (you can write the number on the back of the photo). You will use this for tracking the results of the science project.

Before deciding to use the photographs, it is recommended that you first determine if you can apply the Golden Ratio to them (See resources in bibliography).

Conducting the experiment:

1. Have females rate the male photographs according to level of attractiveness. Use a scale of 1-5 with one being the lowest and five the highest. Note the participant?s response on a note pad for each photograph (Example: Photo graph 1 received a score of 3).
2. Repeat these steps until all female participants have rated the photographs.
3. Repeat this process with the male participants rating the female photographs.

When you have compiled all the data, evaluate each photograph using the Golden Ratio. For example, you could evaluate how your nose, in relation to your mouth, fits the Golden ratio by doing the following:

1. Measure the width of the your nose and as well as the distance between the tip of your nose to your lips.
2. Add the two measurements together to get the sum.
3. Divide the sum by the larger measurement.
4. The closer the final answer is to 1.618, the more your nose will "fit" the Golden Ratio.

(See resource in bibliography for how to calculate the Golden Ration of the face. Start with the article "How to Calculate the Golden Ratio Face," followed with "The Human Face." This article will provide graphics to support the first article). Note: This step can also be performed before conducting the experiment.

Did the photograph or photographs that received the highest ratings have the Golden Ratio?

### Discussion

The Golden Ratio is just one theory that believes all of life has, at a fundamental level, a mathematical composition. Whether it is a human face or a sea shell, the Golden Ratio may explain both its structural pattern as wells its visual appeal. But is this phenomenon inherent in nature or are we simply imposing a perspective on nature that exists only in our own minds, in our attempt to make sense of the world around us?