The Golden Ratio

aka… The Golden Mean, Phi, The Divine

Section, The Golden Cut, The Golden Proportion, The Divine Proportion

The Golden Ratio is an aesthetically pleasing division of space that is often used by artist as the basis for measurement within their compositions.

One of the earliest

examples of the use of the

Golden Ratio is the Great

Pyramid of Giza, built in

2560 BCE

Other Instances of The Golden Ratio •  Greek Mathematician Euclid

(365BC-300BC) mentions the Golden Mean in his “Elements.”

•  Greek Philosopher Plato (424BC-348BC) theorized about the Golden Ratio as a special proportional relationship.

•  Italian Renaissance artist Leonardo da Vinci figured out how the body displays the sectio aurea (Latin=Golden Section) in the 16th Century. The Vetruvian Man,

Leonardo da Vinci

The Fibonacci Sequence

• Leonardo Pisano Fibonacci (b. 1145) • Wrote Liber abaci in 1200 AD, in which he introduced the Latin-speaking world to the decimal number system. • He is BEST known for discovering the Fibonacci Sequence.

The series begins with 0 and 1. After that, use the simple rule: Add the last two numbers to get the next.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc.

The Golden Ratio

•  Begins with the Fibonacci Series… 0,1,1,2,3,5,8,13,21,34,55,89,144

•  If you divide two successive numbers in this series, you will find a common ratio…

5/3= 1.666 8/5= 1.6

13/8= 1.625 etc...

The Golden Ratio

or Phi=1.618

thus

The Golden Rectangle The Golden Rectangle can be formed through the pairing of successive Fibonacci numbers, which can go on forever.

The Golden Spiral

Why do shapes that exhibit the Golden Ratio seem more appealing to the

human eye?

No one really knows for sure.

But we do have evidence that the Golden Ratio seems to be Nature's perfect

number.

Examples in Nature The Fibonacci numbers are Nature's numbering system. They appear everywhere

in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci

numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.

Examples of Art and Architecture

View More Art Examples

Parthenon, Acropolis, Athens The Mona Lisa, Leonardo da Vinci

Notre Dame

Beauty Defined by the Golden Ratio

Who is more “Golden?” In order to determine who is more Golden, we will measure certain aspects of the celebrity faces and then compare ratios. Measure all lengths in centimeters.

a.  Top of Head to Chin b.  Top of Head to Pupil c.  Pupil to Nose Tip d.  Pupil to Lip e.  Width of Nose f.  Outside Distance between Eyes g.  Width of Head h.  Hairline to Pupil i.  Nose Tip to Chin j.  Lips to Chin k.  Length of Lips l.  Nose Tip to Lips

Divide to find the Ratio: 1. A/G= 2. B/D= 3.  I/J= 4.  I/C= 5. E/L= 6. F/H= 7. K/E=

Who has the most Golden Face? Do you find that person more attractive?