The Golden Ratio and Facial Attractiveness

Muliangzi Qu

Presented by:

The golden ratio

• Greek letter phi represents the golden ratio. Its value is:

• The golden ratio is often called the golden section or golden mean.

• Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut and golden number.

calculation

In mathematics and the arts, two quantities are in the golden ratio. If the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one, the geometric relationship is said to be equivalent as the golden ratio. The figure below expressed the relationship algebraically:

First, we need to know:

Applications and observations

Architecture

Many of the proportions of the Parthenon are alleged to exhibit the golden ratio.

Painting

The drawing of a man's body in a pentagram suggests relationships to the golden ratio.

Book design

Many books produced between 1550 and 1770 show these proportions 2:3, 1:√3, exactly, to within half a millimeter

Industrial design

Some sources claim that the golden ratio is commonly used in everyday design, for example in the shapes of postcards, playing cards, posters, wide-screen televisions, photographs, and light switch plates.[

Finance

Nature

The golden ratio and related numbers are used in the financial markets. It is used in trading algorithms, applications, and strategies.

Golden ratio applied to photography with Golden spiral

Facial Attractiveness

• During the European Renaissance, renowned artists and architects used an equation known as the "golden ratio" to map out their masterpieces.

• Thousands of years later, scientists adopted this mathematical formula to help explain why some people are considered beautiful…and others are not.

• Many measurements are used to study facial sex appeal, and one of the measurements is based on the idea of golden ratio.

• These measurements are calculated to determine a person's beauty on a scale of 1 to 10.

First, measures the length and width

of the face. Then, divide the length

by the width. The ideal result—as

defined by the golden ratio—is

roughly 1.6, which means a beautiful

person's face is about 1 1/2 times

longer than it is wide.

Next, measure three segments of

the face—from the forehead

hairline to a spot between the eyes,

from between the eyes to the

bottom of the nose, and from the

bottom of the nose to the bottom

of the chin. If the numbers are

equal, a person is considered more

beautiful.

Finally, statisticians measure other

facial features to determine

symmetry and proportion. On a

perfect face, the length of an ear is

equal to the length the nose, and the

width of an eye is equal to the

distance between the eyes.

Comparison Diagram

Most people score between 4 and 6, and no one has ever been a perfect 10.

Whose face is the most "perfect," according to the measurements? No big surprise here!

Brad Pitt!9.3

Thank you.