#### Transcript of Golden Ratio: A World Of Examples

photo credit Nasa / Goddard Space Flight Center / Reto Stöckli

**A World of Examples**

**The Golden Ratio**

**Art**

"Without Mathematics there is no Art"- Luca Pacioli

Luca Pacioli wrote a book called "De Divina Proportione" (The Divine Proportion). It contains drawings made by Leonardo da Vinci.

da Vinci used the Golden Ratio extensively in his priceless works of art.

Architecture

In architectural literature, the Golden Ratio is referenced frequently.

It is said that the Golden Ratio is responsible for the balance and harmony seen in many important historical buildings.

The famous Greek temple, the Parthenon, is one of the most recognized examples of ancient architecture mostly based in the use of the Golden Ratio.

Human Body

The human body is based on patterns of 5. The Greek letter Phi is derived from many mathematical equations based on the number 5.

5 openings to the face, 5 appendages on each hand and foot, 5 senses etc.

The DNA molecule is based on the Golden Ratio. It measures 34 angstroms long by 21 angstroms wide. 21 and 34 are both in the Fibonacci series and their ratio, 1:6190 is very close to 1:6180, the value of Phi.

Nature

Many examples of the the Golden Ratio are found in nature. For example, the curve in a sea shell follows the curve of the Fibonacci Spiral almost exactly.

Plants grow new cells in spirals, such as the pattern of seeds in a sunflower.

Seeds are produced at the center and rotate upwards and outwards.

The spirals naturally produced in flowers or vegetables like lettuce happen because each new plant cell is formed after a turn.

Apple Logo Golden Ratio Diagram

Leonardo da Vinci's "Mona Lisa" in the Golden Spiral

A front view of the Parthenon shows the obvious use of the Golden Ratio

The Pyramid of Giza diagrammed using Phi , the Greek letter representing the irrational number 1.618, which is the numerical value of the Golden Ratio

The ratio of one's hand to forearm is approximately the Golden Ratio value.

The ratio of the minor groove to the major groove is the same as the value of Phi

This rose and sunflower are perfect examples of the Fibonacci Spiral

Romanesque Broccoli with extremely defined spirals

Mathematical proportion for the Golden Ratio

Phi

The Continuous value of Phi

One of Earth's most powerful forces conforms to the Golden Ratio

A Spiral Galaxy contains the aspects of the Golden Ratio

This sea shell conforms almost perfectly to the Fibonacci Spiral

Full transcript