# Investigating Beauty with the Golden Ratio

Contents

Investigating Beauty with the Golden Ratio

# Abstract

Two irrational numbers (approximately 0.618 and 1.618), are often referred to as the “golden ratio.” These two numbers possess many intriguing properties. For example, shapes that adhere to the golden ratio have long been considered to be aesthetically pleasing. This experiment will investigate whether the golden ratio can be used to predict peoples’ assessment of beauty in others.

# Hypothesis

Do test subjects consider celebrities with facial measurements that come closest to the golden ratio to be the most attractive?

# Background Research

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,

where the Greek letter phi ( or ) represents the golden ratio. Its value is:

A001622

The golden ratio is also called the golden mean or golden section (Latin: sectio aurea). Other names include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, and golden number.

Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.
Materials List

·         Images of well-known celebrities

·         Ruler

·         Calculator

·         Computer

·         Printer

·         Notebook for analyzing results

# Experimental procedure

1.    Perform an online search for images of famous people. Include celebrities that you find attractive and celebrities that you find unattractive.

2.    Enlarge the images so that you have a clear view of the front of the celebrity’s face, and print your images.

3.    Measure and record the following aspects of each person’s face, to the nearest tenth of a centimeter: (A) Top of the head to the chin; (B)Top of the head to the pupil; (C) Pupil to the tip of the nose; (D) Pupil to the lip; (E) Width of the nose; (F) Outside distance between the eyes; (G) Width of the head; (H) Hairline to the pupil; (I) Tip of the nose to the chin; (J) Lips to the chin; (K) Length of the lips; (L) Tip of the nose to the lips

4.    Calculate the following ratios for each celebrity:

o    A/G

o    B/D

o    I/J

o    I/C

o    E/L

o    F/H

o    K/E

5.    Create a survey that evaluates the attractiveness of each celebrity image on a scale of 1 to 10.

6.    Show 20+ test subjects your images and ask them to take the survey.

7.    Evaluate your results. Based on your calculations, which celebrity images came closest to being “golden”? Did these celebrities receive the highest rankings for attractiveness in the surveys taken by your test subjects?

# Conclusions

In conclusion, we can find the supposedly beauty knowing the measures of the golden ratio. Some people may have the exact measure and others not, but that does not infers a lot in it in their beauty profile.