Table of contents.

Contents

Investigating
Beauty with the Golden Ratio

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.

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

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

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?

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.