THE GOLDEN

RATIO By: Natasha Minichino & Anna Gisone

Class 702

The Golden Rectangle

A Golden Rectangle is a rectangle in which the ratio of the length to the width is the Golden Ratio. The Ratio is equal to 1.618033988749894842, or 1.62.

In other words: What ever the width of the rectangle is,

multiply it by 1.62 to get the length.

DID YOU KNOW ??? If you have a Golden Rectangle and

you cut a square off it so that what remains is a rectangle, that remaining rectangle will also be a Golden Rectangle. You can keep cutting these squares off and getting smaller and smaller Golden Rectangles.

For Example . . . . . . . .

As you can see, no matter how may times

you cut squares out of a golden rectangle, you will still end up with a golden rectangle.

HISTORYThe Golden Rectangle has been admired and

used since ancient times. The reason for the golden rectangle's charm is that it is considered to be one of the most pleasing shapes to look at. Our human eye perceives the golden rectangle as an especially beautiful geometric form.

ANCIENT GREECE Ancient Egyptians, Mesopotamians

and Greeks were aware of the beauty of the Golden Rectangle and used it to create many different buildings. One of the most famous and beautiful buildings, built in ancient Greece on the Acropolis, is called the Parthenon. It was created about 2500 years ago.

Just as the golden rectangle was pleasing to ancient Greeks, it is still pleasing to modern day Americans.

The Human Face Plastic surgeons have used the golden

section and some of its relatives to make a mask that he claims is the most beautiful shape a human face can ever have, it used decagons and pentagons as its function that embodies phi in all other dimensions. The most beautiful faces are the ones that are the most easily recognizable as human.

THE HUMAN SMILE

The prefect smile; the two front teeth form a golden rectangle (which is said to be one of the most visual, satisfying, of forms, as it is formed with sides of 1 and 1.618.)

A= 17 B= yIn order to find the length, multiply 17 by 1.62.

1.62x 1727.54

Activity !- Use a tape measure.- Measure from your pupil to your chin.- Then, Measure your forehead. - Then divide the two measurements.- If you get an answer close to 1.62, your face is almost

considered a golden face.

BIBLIOGRAPHY• http://mathforum.org/dr.math/faq/faq.golden

.ratio.html• http://cuip.uchicago.edu/~dlinarain/golden/ac

tivity8.htm• http://library.thinkquest.org/trio/TTQ05063/p

hibeauty1.htm